Southampton left it late to beat Crystal Palace, Tim Sherwood's first Aston Villa win came in dramatic circumstances against rivals West Brom while Gus Poyet was sent off as Sunderland fought back for a point at Hull City.
Southampton leapfrogged Liverpool back into fifth place as Sadio Mane scored to defeat Crystal Palace 1-0.
Palace came close to making a breakthrough on 55 minutes only for Wilfried Zaha to hit the post after Fraser Forster had denied Yannick Bolasie.
Southampton's winner came in the 83rd minute as goalkeeper Julian Speroni spilled James Ward-Prowse's shot to allow Mane to tap home.
Christian Benteke scored an injury-time penalty to ensure Sherwood's Aston Villa beat midlands rivals West Brom 2-1.
Gabriel Agbonlahor put Villa in front on 22 minutes when he latched onto Christian Benteke's header to slide the ball past goalkeeper Ben Foster.
Villa were unfortunate not to double their advantage in the first half when Agbonlahor saw his effort just scrambled off the line by Foster before Fabian Delph hit the post with a curling effort.
West Brom hit back on 66 minutes through Saido Berahino, who scored his 12th league goal of the season with a header from close range after Joleon Lescott guided the ball back across the goal.
With seconds remaining, Foster brought Matthew Lowton down in the box, and Benteke stepped up to coolly roll home the winner to boost VIlla's survival hopes.
Jack Rodwell clinched a point for Sunderland at Hull as the game at the KC Stadium ended 1-1.
Hull took the lead on 15 minutes as Dame N'Doye scored this third Premier League goal for the club, skillfully flicking into the net via Tom Huddlestone's low delivery from a free kick.
Matters got heated on the touchline when Sunderland manager Gus Poyet was sent to the stands after he clashed with counterpart Steve Bruce.
With 13 minutes left on the clock, Patrick van Aanholt's cross found Rodwell who headed in to secure a point.