Sunderland eased their own lingering relegation concerns by beating Burnley 2-1 at the Stadium of Light, whilst Wolves and Bolton begin to look safe. Burnley though remain in the bottom three and look certain for a quick return to the Championship.
Fraizer Campbell and Darren Bent scored the goals at the Stadium of Light to put the host's two-up at the break.
Steven Thompson pulled a goal back in the 82nd minute, to set up a nervy last few minutes but the Black Cats held on.
Hull, who are in the drop-zone with Burnley, were held 0-0 at Birmingham.
Craig Gardner, Cameron Jerome and Lee Bowyer went close for the Blues whilst Jan Vennegoor of Hesselink almost netted for the Tigers with a diving header from Andy Dawson's cross.
In fact Hull could have won it in stoppage time but Craig Fagan's thumping volley flashed wide.
Bolton left it late to all but secure Premier League football next season with a 2-1 win at Stoke.
Stoke led 1-0 after Dave Kitson prodded the ball past a stranded Jussi Jaaskelainen before slotting home early in the first half.
Rory Delap's long throw was then headed against the post by Robert Huth.
But Matt Taylor equalised five minutes from time with a free-kick, taking a slight deflection off Ricardo Fuller en route, and then scored the winner three minutes later from substitute Vladimir Weiss' cross.
Twice the Toffees took the lead but Rovers were intent on maintaining their impressive home record and battled back twice to equalise.
Tim Cahill though had the last word for the visitor's with a 90th minute winner.
Mikel Arteta's fourth-minute penalty gave Everton lead after being brought down by Ryan Nelsen's reckless challenge - though he was later lucky to escape a red card after appearing to poke Morten Gamst Pedersen in the eye.
Rovers' Steven Nzonzi blasted a 68th minute swerving 30-yard shot past Tim Howard.
Another replacement, Jason Roberts, levelled two minutes later - only for the Australian to then tap in Yakubu's low cross.
Wolves continue to edge away from the relegation spots in a dour 0-0 draw at Fulham's Craven Cottage.
Earlier in the day Paul Scholes headed an injury time winner in the Manchester derby as United triumphed 1-0 over City at Eastlands to complete the double over the rivals this season.