Our attention also turns to cup business tomorrow, when a new name will be engraved on the Petrofac Training Cup trophy.
Rangers, already having clnched the Championship title, face Peterhead, second in League One and themselves chasing promotion, at a sold-out Hampden.
Join us then for more live action.
Fat lady singing?
Dundee United manager Mixu Paatelainen is not yet prepared to accept that relegation is a certainty.
At least the Terrors have some respite next weekend, when they can turn their attention to the Scottish Cup semi-final against Hibernian at Hampden.
Intriguing that it is a match between two sides suffering in the league campaigns in recent weeks.
Dundee United manager Mixu Paatelainen
Dundee United 0-2 Inverness CT
"At half-time, it was nowhere good enough - a poor performance. Diabolical.
"All credit to Inverness, they wanted to be first on the ball.
"It will be very hard and has been very hard for a long time, but obviously we keep fighting and keep believing.
"Today was a major disappointment, the way we performed, and we can't accept performances like that."
Couple of firsts
Hamilton's win was their first at home in eight months - their last victory at New Douglas Park being 19 September.
Meanwhile, Kilmarnock's win was their first in their seven games under manager Lee Clark.
Ross County manager Jim McIntyre
Ross County 1-0 Partick Thistle
"We made it no secret that our goal was to get into the top six after fighting relegation in the last two seasons.
"It is fantastic and we deserve it and this is for the chairman, who has given me great backing.
"We dropped out of it last week after being in the top six for most of the season, but we knew that, with the importance of the games for the other teams, we had a chance.
"We had to scrap out there as Thistle put us under a lot of pressure."
Sorry Shire
In League Two, East Stirlingshire's 3-0 defeat at home to Queen's Park means that the losers will definitely face a play-off to retain their place in the Scottish Professional Football League.
At the top, Gary Naysmith's East Fife moved seven points clear with only three games remaining with a 3-0 win over Montrose.
Annan Athletic move into second on goal difference over Clyde after their 4-1 victory over Arbroath.
Barry Ferguson's Clyde slumped to another painful defeat, beaten 3-0 by Berwick Rangers and are only a point above Queen's Park and Elgin City, who drew away to Stirling Albion.
Inverness CT manager John Hughes
Dundee United 0-2 Inverness CT
"Fantastic victory. Good result coming here and we are delighted with the performance.
"Results have went against us and we are in that bottom six.
"I would have more of that if I had players at my disposal who have moved on or who have been injured.
"We can't feel sorry four ourselves and, with competition for places, I think we can get that every week."
League One round-up
In League One, promotion hopefuls Ayr United suffered a blow with a 1-0 defeat at home to Albion Rovers.
At the bottom, Forfar Athletic edged a point clear of Brechin City after a fine 2-2 draw away to champions Dunfermline Athletic.
Brechin were beaten by Cowdenbeath, who move above Stenhousemuir, who drew 1-1 with Stenhousemuir, into fourth bottom.
Hibs horror
In the Championship, Hibernian's slump in form continued with a 1-0 defeat away to already-relegated Alloa Athletic, thanks to Michael Duffy's first-half strike.
Second-top Falkirk overcame St Mirren in a five-goal thriller to move six points clear of Hibs in the race for promotion play-off places.
Hibs still have two games in hand, but the Bairns have the points in the bag ahead of the two rivals meeting at Easter Road on Tuesday.
LEAGUE TWO FULL-TIME SCORES
Annan Athletic 4-1 ArbroathBerwick Rangers 3-0 ClydeEast Fife 3-0 MontroseEast Stirlingshire 0-3 Queen's ParkStirling Albion 0-0 Elgin City
Alloa Athletic 1-0 HibernianFalkirk 3-2 St MirrenMorton 2-1 LivingstonQueen of the South 1-2 Raith Rovers
Nightmare for Terrors
It was an awful day for Dundee United. On top of their own defeat at home to Inverness Caley Thistle, all three of the teams above them won.
Second-bottom Kilmarnock move eight points clear with only 15 points available in the remaining matches.
Hamilton are another four points further ahead, with Caley Thistle 15 points clear of bottom spot.
Bottom six
Dundee
Partick Thistle
Inverness Caledonian Thistle
Hamilton Academical
Kilmarnock
Dundee United
Top six
Celtic
Aberdeen
Hearts
Motherwell
St Johnstone
Ross County
Top six confirmed
Hamilton's win over Dundee means that Paul Hartley's visitors drop out of the top six and are leapfrogged by Ross County.
Partick Thistle's failure to find an equaliser against County means that they and Inverness Caley Thistle miss out on the top six.
A goal for the Glasgow side would have meant that Inverness, who defeated Dundee United, would still have had a chance to clinch their place against Hearts next week.
Live Reporting
Clive Lindsay
All times stated are UK
Get involved
Latest PostCup fever
Our attention also turns to cup business tomorrow, when a new name will be engraved on the Petrofac Training Cup trophy.
Rangers, already having clnched the Championship title, face Peterhead, second in League One and themselves chasing promotion, at a sold-out Hampden.
Join us then for more live action.
Fat lady singing?
Dundee United manager Mixu Paatelainen is not yet prepared to accept that relegation is a certainty.
At least the Terrors have some respite next weekend, when they can turn their attention to the Scottish Cup semi-final against Hibernian at Hampden.
Intriguing that it is a match between two sides suffering in the league campaigns in recent weeks.
Dundee United manager Mixu Paatelainen
Dundee United 0-2 Inverness CT
"At half-time, it was nowhere good enough - a poor performance. Diabolical.
"All credit to Inverness, they wanted to be first on the ball.
"It will be very hard and has been very hard for a long time, but obviously we keep fighting and keep believing.
"Today was a major disappointment, the way we performed, and we can't accept performances like that."
Couple of firsts
Hamilton's win was their first at home in eight months - their last victory at New Douglas Park being 19 September.
Meanwhile, Kilmarnock's win was their first in their seven games under manager Lee Clark.
Ross County manager Jim McIntyre
Ross County 1-0 Partick Thistle
"We made it no secret that our goal was to get into the top six after fighting relegation in the last two seasons.
"It is fantastic and we deserve it and this is for the chairman, who has given me great backing.
"We dropped out of it last week after being in the top six for most of the season, but we knew that, with the importance of the games for the other teams, we had a chance.
"We had to scrap out there as Thistle put us under a lot of pressure."
Sorry Shire
In League Two, East Stirlingshire's 3-0 defeat at home to Queen's Park means that the losers will definitely face a play-off to retain their place in the Scottish Professional Football League.
At the top, Gary Naysmith's East Fife moved seven points clear with only three games remaining with a 3-0 win over Montrose.
Annan Athletic move into second on goal difference over Clyde after their 4-1 victory over Arbroath.
Barry Ferguson's Clyde slumped to another painful defeat, beaten 3-0 by Berwick Rangers and are only a point above Queen's Park and Elgin City, who drew away to Stirling Albion.
Inverness CT manager John Hughes
Dundee United 0-2 Inverness CT
"Fantastic victory. Good result coming here and we are delighted with the performance.
"Results have went against us and we are in that bottom six.
"I would have more of that if I had players at my disposal who have moved on or who have been injured.
"We can't feel sorry four ourselves and, with competition for places, I think we can get that every week."
League One round-up
In League One, promotion hopefuls Ayr United suffered a blow with a 1-0 defeat at home to Albion Rovers.
At the bottom, Forfar Athletic edged a point clear of Brechin City after a fine 2-2 draw away to champions Dunfermline Athletic.
Brechin were beaten by Cowdenbeath, who move above Stenhousemuir, who drew 1-1 with Stenhousemuir, into fourth bottom.
Hibs horror
In the Championship, Hibernian's slump in form continued with a 1-0 defeat away to already-relegated Alloa Athletic, thanks to Michael Duffy's first-half strike.
Second-top Falkirk overcame St Mirren in a five-goal thriller to move six points clear of Hibs in the race for promotion play-off places.
Hibs still have two games in hand, but the Bairns have the points in the bag ahead of the two rivals meeting at Easter Road on Tuesday.
LEAGUE TWO FULL-TIME SCORES
Annan Athletic 4-1 ArbroathBerwick Rangers 3-0 ClydeEast Fife 3-0 MontroseEast Stirlingshire 0-3 Queen's ParkStirling Albion 0-0 Elgin City
LEAGUE ONE FULL-TIME SCORES
Airdrieonians 1-1 StenhousemuirAyr United 0-1 Albion RoversCowdenbeath 2-1 Brechin CityDunfermline Athletic 2-2 Forfar Athletic
CHAMPIONSHIP FULL-TIME SCORES
Alloa Athletic 1-0 HibernianFalkirk 3-2 St MirrenMorton 2-1 LivingstonQueen of the South 1-2 Raith Rovers
Nightmare for Terrors
It was an awful day for Dundee United. On top of their own defeat at home to Inverness Caley Thistle, all three of the teams above them won.
Second-bottom Kilmarnock move eight points clear with only 15 points available in the remaining matches.
Hamilton are another four points further ahead, with Caley Thistle 15 points clear of bottom spot.
Bottom six
Dundee
Partick Thistle
Inverness Caledonian Thistle
Hamilton Academical
Kilmarnock
Dundee United
Top six
Celtic
Aberdeen
Hearts
Motherwell
St Johnstone
Ross County
Top six confirmed
Hamilton's win over Dundee means that Paul Hartley's visitors drop out of the top six and are leapfrogged by Ross County.
Partick Thistle's failure to find an equaliser against County means that they and Inverness Caley Thistle miss out on the top six.
A goal for the Glasgow side would have meant that Inverness, who defeated Dundee United, would still have had a chance to clinch their place against Hearts next week.
FULL-TIME
Dundee United 0-2 Inverness Caledonian Thistle
FULL-TIME
Hamilton Academical 2-1 Dundee
FULL-TIME
Kilmarnock 3-0 St Johnstone
FULL-TIME
Ross County 1-0 Partick Thistle