|Gloucester (14) 14|
|Tries: Sharples, Meakes Cons: Laidlaw (2)|
|Connacht (0) 7|
|Tries: Penalty Cons: Carty|
Gloucester held on to overcome Connacht and reach the European Challenge Cup semi-finals.
The English side, winners of the competition in 2006, were led by the creativity of James Hook and will face Exeter or Newcastle in the final four.
Hook was central to both Gloucester tries, helping release Charlie Sharples and then Billy Meakes to touch down.
Connacht improved and forced a late penalty try, but the hosts were strong in the closing minutes.
The Challenge Cup, in a new guise this season after an overhaul of European competitions, had offered the only prospect of silverware this year for both sides, with neither team in the play-off picture in the Premiership and Pro12 respectively.
And while the Cherry and Whites have struggled domestically, they have now won seven from seven in Europe, albeit after enduring late pressure from Connacht at Kingsholm.
In a game of few clear openings, Hook led a breakaway and the ball found Sharples for the opening score, before the fly-half's chipped kick bounced nicely for Meakes to finish, with Greig Laidlaw converting twice.
But Gloucester allowed Connacht territory after the interval and, with the Irish province finding joy at the maul, they were rewarded with a penalty try when Robbie Henshaw looked like he was set to touch down from a drive.
Jack Carty knocked over the extras, only for Gloucester to hold firm in the final 15 minutes and progress after going out at this stage in the last two seasons.
Gloucester director of rugby David Humphreys told BBC Radio Gloucestershire:
"The initial reaction is one of relief - we got ourselves in a good position. I thought we played some very good rugby in the first half.
"Coming off a five-day turnaround it was always going to be a challenge but I thought we responded very well to that.
"Second half I suppose more credit to Connacht. They played well, kept the ball and caused us some problems, but ultimately the defence won us the game."
Gloucester: McColl; Sharples, Meakes, Twelvetrees (capt), May; Hook, Laidlaw; Murphy, Hibbard, Afoa, Savage, Palmer, Kalamafoni, Kvesic, Evans.
Replacements: Dawidiuk, Wood, Puafisi, Hudson, Moriarty, Robson, Burns, Purdy.
Connacht: Muliaina; O'Halloran, Poolman, Henshaw, Healy; Carty, Marmion; Buckley, McCartney, Ah You, Roux, Muldowney, Browne, Masterson, Muldoon (capt).
Replacements: Delahunt, Cooney, Bealham, Naoupu, Connolly, Porter, Ronaldson, Leader.
Referee: Mathieu Raynal