Ryan Giggs enjoyed the perfect start to his interim Man United career with a big win at home to Norwich, but Everton's Champions League hopes took a big knock and Fulham threw away the chance to move out of the relegation zone.
Wayne Rooney and Juan Mata both scored twice as Man United cantered to a 4-0 win over Norwich City.
Giggs assumed temporary control of United on Tuesday following the sacking of David Moyes. Although the United board are searching for an experienced successor, Giggs has made no secret of his desire to become full-time manager. And the 40-year-old interim manager did his chances no harm with this display.
Once United had put a slightly cumbersome first half behind them, they strolled to victory. Steven Whittaker pulled Danny Welbeck down in the box four minutes before the interval and Rooney made no mistake from the spot to open the scoring.
Rooney added a second soon after the restart before Juan Mata came off the bench to score twice from close range as United coasted home.
Hull City fought back from two goals down to draw 2-2 with Fulham at Craven Cottage and stop the hosts from moving out of the relegation zone.
Ashkan Dejagah broke the deadlock on 55 minutes, cutting inside and curling the ball into the top corner from the edge of the area. Then just three minutes later, Fernando Amorebieta guided in a glancing header from Kieran Richardson's cross.
However, Nikica Jelavic pulled one back for Hull, nodding in a rebound from a David Stockdale save, and Shane Long then headed in Sone Aluko's cross with three minutes remaining to leave Fulham a point from safety with two games remaining.
Swansea City eased any lingering relegation fears by securing a 4-1 win at home to Aston Villa, who slumped to a fifth defeat in six games and are now just four points above the drop zone.
Wilfried Bony put Swansea in front after 10 minutes, slotting Jonjo Shelvey's ball past Brad Guzan for his 23rd goal of the season.
Gabriel Agbonlahor brought Villa level on 22 minutes, meeting Marc Albrighton's cross from six yards. However, Shelvey quickly restored Swansea's lead with a goal-of-the-season contender, sending a dipping shot from the edge of the centre circle over the back-tracking Guzan.
Pablo Hernandez then added his side's third, controlling Shelvey's cross at the far post and curling home, before Bony converted a late penalty after Marvin Emnes was bundled over in the box by Nathan Baker.
West Bromwich Albion, meanwhile, continued their survival charge with a vital 1-0 win at home to West Ham United, with Saido Berahino converting from Morgan Amalfitano's cross early on. The result moved them five points clear of 18th-placed Fulham.
Two calamitous own goals put a serious dent in Everton's bid for Champions League football as they fell to a 2-0 defeat at Southampton.
Making just his sixth appearance this season alongside John Stones at centre-back, Antolin Alcaraz headed past Tim Howard into his own net with 53 seconds gone at St Mary's.
Seamus Coleman then followed suit on 31 minutes, steering Nathaniel Clyne's cross from the right past Howard into the bottom corner.
Everton have now lost two of their four games since beating Arsenal 3-0 at Goodison Park earlier this month. They remain a point behind Arsenal in the race for fourth place and have played a game more than Arsene Wenger's side, who face Newcastle at home on Monday night.
Tottenham Hotspur tightened their grip on sixth place and qualification for the Europa League with a hard-fought 1-0 victory over Stoke City at the Britannia Stadium.
Spurs' winner came from an unlikely source when defender Danny Rose headed home Emanuel Adabayor's cross at the far post.
It was Rose's first goal since scoring a memorable volley against Arsenal on his Premier League debut as a 19-year-old almost four years ago to the day.