Down boosted their hopes of promotion from Division Three with a 0-17 to 0-9 win over Offaly while Derry were beaten 3-13 to 3-11 by Cork.
Barry O'Hagan scored six points for the Mourne side in Tullamore and Down sit third and three points off the top.
Derry's fightback against the leaders at Pairc Ui Chaoimh fell short and they have it all to do to secure promotion.
Teams outside the top two will play in the second-tier championship unless they make their provincial final.
Down are level on seven points with second-placed Longford after a comfortable win against Offaly at O'Connor Park.
The Ulster victors stormed to a 0-11 to 0-2 lead at the break and Offaly never threatened a comeback despite outscoring Down in the second half.
O'Hagan fired over five first-half points and James Guinness added three while Celium Doherty, Liam Kerr and Corey Quinn were also on target for Down.
Offaly scored six of the opening nine points in the second half, with Ruairi McNamee bagging three before the hosts had Eoin Carroll dismissed for two yellow cards.
Connaire Harrison popped over a point and then struck the Offaly crossbar as Down eased to victory.
It was a different story for Derry and the prospect of second-tier championship football is looming large after this narrow defeat.
A mistake by Derry keeper Odhran Lynch gifted Damien Gore the opening goal and Cork went in 1-5 to 0-4 in front at half-time.
John O'Rourke netted for the Rebels early in the second half but a fine Niall Loughlin goal kept Derry in touch.
O'Rourke completed his double to put nine points between the sides with 10 minutes left but there was still life in the Oak Leafers.
Emmett Bradley hit the Cork net and it was soon followed by a Patrick Kearney goal but Cork held on for a two-point win.
What they said
Derry boss Rory Gallagher: "We were lucky to be only two points down at the final whistle.
"Cork dominated possession - we couldn't get our hands on the ball and gave us a lesson in the middle of the field."
Down manager Paddy Tally: "I'm satisfied but we're also a bit disappointed we didn't get more on the scoreboard.
"We had a couple of goal chances and it would have been a nice way to round it off but but you have to be satisfied with the result and the two points on the board."
ALLIANZ FOOTBALL LEAGUE RESULTS