On a day when Ryan Giggs won his first game in charge of Manchester United, Fulham had to settle for a draw against Hull City and West Bromwich Albion and Swansea City claimed crucial wins.
In the day's early kick-off, Everton missed the chance to go fourth as a couple of own goals helped Southampton do Arsenal a massive favour at St Mary's.
Jonjo Shelvey scored one of the goals of the season as Swansea piled the pressure on Aston Villa, while West Brom pulled five points clear of the bottom three with a win over West Ham.
Fulham are still in the relegation zone after conceding two late goals at home to Hull, while Tottenham Hotspur edged out Stoke City.
Norwich City are now just a point above the bottom three after losing 4-0 to Manchester United in a game which marked the start of Giggs' temporary reign.
Having sacked David Moyes in midweek and denied reports on Saturday morning that a deal to bring in Louis van Gaal had already been agreed, the spotlight was on Giggs in the dugout after he was handed the job on an interim basis until the end of the season.
It was Giggs' opposite number, Neil Adams, though, who most desperately needed to deliver a result to push Norwich up the table, and it was to prove a frustrating night at Old Trafford as Wayne Rooney and Juan Mata scored two apiece in a convincing home win.
The England striker made it 1-0 from the penalty spot four minutes before half-time after Danny Welbeck had been pulled back by Steven Whittaker, and added a second on 48 minutes as he drove a shot into the bottom corner from 25 yards despite slipping as he struck the ball.
Mata came on in the 60th minute and found the net just three minutes later as he steered home a Phil Jones cross, before nodding in United's fourth from point-blank range after 73 minutes.
The battle to avoid the drop took several twists and turns in a key game at Craven Cottage as Fulham surrendered a two-goal advantage and were pegged back to 2-2 by Hull to remain in the relegation zone.
A tight first half finished goalless, although Hull had a strong penalty appeal waved away when referee Lee Mason decided that Fernando Amorebieta had not brought down Shane Long.
Felix Magath's side then opened the scoring in the 55th minute as half-time substitute Ashkan Dejagah weaved away from a couple of defenders to drift in from the right and curled an exquisite shot into the top corner.
Amorebieta's doubled Fulham's advantage just three minutes later with a glancing header from Kieran Richardson's inviting cross, but Hull responded brilliantly to salvage a point.
Nikica Jelavic reduced the arrears when he reacted quickly to beat David Stockdale after Sascha Riether had deflected the ball on to his own bar, and Shane Long headed home Sone Aluko's cross three minutes from time to deny Fulham a precious victory which would have lifted them out of the bottom three.
West Brom boosted their survival hopes with a 1-0 win over West Ham at The Hawthorns.
Saido Berahino made the crucial breakthrough in the 11th minute with a close-range finish from Morgan Amalfitano's cross, after great work from Stephane Sessegnon to lead a swift counter-attack and burst through a couple of challenges.
The Hammers were unable to find an equaliser but results elsewhere leave them with a six-point cushion over the bottom three, while West Brom are now just a point further back.
Aston Villa slipped deeper into trouble as they lost 4-1 to Swansea at the Liberty Stadium in a match which featured a remarkable Shelvey goal from about 45 yards.
Swansea eased their own relegation fears with a win at Newcastle United last weekend and took the lead against Aston Villa after just 10 minutes as Wilfried Bony beat the offside trap to latch on to Shelvey's pass and calmly slot home for his 14th league goal of the season in all competitions.
Gabriel Agbonlahor turned in Marc Albrighton's excellent right-wing cross from just a couple of yards out to equalise in the 22nd minute, but Villa were back on level terms for just four minutes before Shelvey produced his moment of magic.
With a strike reminiscent of Rooney's goal against West Ham United last month, Shelvey controlled the ball on his chest just inside the centre circle and spotted Brad Guzan off his line before unleashing a dipping, swerving volley which flew into the top corner.
Pablo Hernandez's calm finish extended Swansea's lead in the 73rd minute and Bony added a late penalty after Nathan Baker had clattered into Marvin Emnes.
The result leaves Garry Monk's side on 39 points, while Villa are just four clear of the drop zone.
Everton's bid for Champions League qualification suffered a huge setback as they went down 2-0 at Southampton to stay behind Arsenal, who can now move four points clear in fourth place with a win over Newcastle United on Monday.
Southampton produced an impressive performance but much of the damage was self-inflicted by Everton, with Antolin Alcaraz scoring an own goal inside the opening minute at St Mary's as he headed in a Rickie Lambert cross.
Seamus Coleman repeated Alcaraz's mistake in the 31st minute when Nathaniel Clyne swung over a cross from the right and he inadvertently nodded past Tim Howard, leaving Southampton firmly in control.
Everton battled back after the break and thought they should have had a penalty when Leon Osman went down in the box under a tackle from Dejan Lovren, but referee Michael Oliver felt it was a dive and yellow carded the midfielder.
Danny Rose had an eventful afternoon as he scored the only goal of the game at Stoke to keep Tottenham on course for a European spot.
Rose powered in a header on 33 minutes after Emmanuel Adebayor had cleverly skipped away from Glenn Whelan, poking the ball one side of his opponent and darting past him on the other before pulling back an accurate cross.
Stoke's chances of mounting a comeback were severely hit early in the second half when Ryan Shawcross was dismissed for a second bookable offence after a foul on Rose, which riled the Britannia Stadium crowd but looked a fair decision by referee Andre Marriner.
The Stoke fans booed Rose's every touch and he pushed Geoff Cameron in frustration after a foul to earn himself a booking before eventually being replaced, and Spurs had to withstand a late onslaught against 10 men to emerge triumphant.