Everton kept their top four hopes alive with a 3-2 win at home to Swansea that moved them up to fifth place while Norwich and Hull boosted their bids to avoid relegation with vital wins.
Leighton Baines maintained his 100% record from the penalty spot for Everton in the Premier League, scoring his 12th to put the hosts in front after Chico Flores brought down Ross Barkley in the box.
However Wilfried Bony grabbed his 18th goal of the season to level the scores, converting Angel Rangel's square ball from close range on 33 minutes.
But Romelu Lukaku restored Everton's lead eight minutes after the restart, meeting Kevin Mirallas' return pass and finding the back of the net.
Five minutes later Barkley made it 3-1, stooping to nod in Mirallas' corner at the far post.
Ashley Williams pulled one back for Swansea in added time with a header from a corner but it proved to be too little, too late.
Norwich eased the pressure on manager Chris Hughton with a 2-0 win over relegation rivals Sunderland at Carrow Road.
A howler from Wes Brown allowed Norwich to take the lead, the defender passing straight to Johan Elmander who squared the ball for Robert Snodgrass to fire in low in the 20th minute.
Alex Tettey then doubled Norwich's lead just past the half-hour mark, meeting John O'Shea's headed clearance with a first-time volley from 30 yards that sailed into the top corner.
Sunderland manager Gus Poyet wasted no time by making two changes before the break, hooking Jack Colback and Ki Sung-Yueng for Lee Cattermole and Sebastian Larsson. Cattermole then managed to get booked three minutes after coming on.
But the visitors failed to get themselves back into the match before Marcos Alonso was sent off for a second yellow in stoppage time.
Hull also secured three crucial points with a 2-0 win at home to West Brom.
The hosts were awarded a penalty after Craig Dawson brought down Shane Long, with Liam Rosenior nodding home the rebound after Nikica Jelavic saw his spot-kick saved by Ben Foster.
Long then made it 2-0 against his former side with a left-footed volley from six yards out seven minutes from the interval but his celebrations were muted.
Newcastle snatched a dramatic 1-0 win at home to Crystal Palace with Papiss Cisse striking in added time.
Yannick Bolasie came close to giving the visitors the lead when his second-half shot struck the crossbar, before Cisse broke Palace's hearts by heading home Hatem Ben Arfa's cross at the death.