Leaders Manchester City host second-placed Liverpool on Monday, leaving the focus of Sunday's games on the battle for the fourth Champions League spot.
United suffered a 1-0 loss to struggling Everton at Goodison Park while Arsenal were handed a surprise 2-1 home defeat by Brighton & Hove Albion.
Son Heung-min struck a superbly taken hat-trick as Tottenham Hotspur took a grip on fourth place, romping to a 4-0 win at Aston Villa.
With Arsenal losing earlier on Saturday, Spurs have a three point lead over their North London rivals with 57 points from 31 games - the Gunners have played one game less.
Arsenal are also on 54 points with West Ham United and Manchester United both on 51 points.
Out of all cup competitions, United needed a victory at Frank Lampard's struggling Everton to kick-start their bid to return to the Champions League.
But after a promising start from the visitors it was Everton who grabbed the lead through Anthony Gordon's shot which deflected off Harry Maguire and beat the wrong-footed David De Gea in the United goal.
Everton, whose defeat at Burnley in midweek had left them a point and a place above the relegation zone, showed real grit and determination to hang on to their lead while United looked totally lacking in a coherent game plan.
A late Cristiano Ronaldo effort was as close as United came to an equaliser as they slipped to a loss that left English football's most successful club languishing seventh in the table.
Everton moved four points clear of 18th-placed Burnley, who travel to Norwich City on Sunday.
Arsenal suffered a second straight loss as Brighton ended their seven-match winless run with Zambian midfielder Enock Mwepu scoring one goal and creating another.
Brighton opened the scoring when a long ball found Mwepu on the flank and he picked out Leandro Trossard who curled past Aaron Ramsdale.
Arsenal made tactical shifts that showed signs of turning the game around but they were dealt a decisive blow when Mwepu drilled home a half-volley from the edge of the box.
Martin Odegaard provided a late slither of hope in the 89th minute with a long-range shot that took a wicked deflection and looped over goalkeeper Robert Sanchez to give Arsenal a lifeline, but Brighton held on.
Chelsea manager Thomas Tuchel was furious with his team's performance in their 3-1 loss at home to Real Madrid in the Champions League but get the desired reaction from his players.
Two goals each by Timo Werner and Mason Mount and first- half strikes by Marcos Alonso and Kai Havertz sealed a 6-0 demolition job at St Mary's Stadium.
Chelsea went up 1-0 in the eighth minute as Alonso ran on to a deft flick by Mount and blasted in his first league goal since the opening day of the campaign.
Mount, Chelsea's leading scorer in the league this season, equalled his tally of nine goals from the previous campaign with a superb shot from outside the box after Southampton's shaky defence failed to deal with Ruben Loftus-Cheek's cross.
Werner made up for earlier misses by beating Jan Bednarek for pace before rounding Fraser Forster and finishing into an empty net and Havertz swept in Chelsea's fourth.
A relentless Chelsea were rewarded again after the break as Werner tapped in a rebound from N'Golo Kante's effort which was saved by Forster and Mount completed the rout.
American manager Jesse Marsch saw his Leeds United take a big step towards Premier League survival with a 3-0 victory over Watford at Vicarage Road.
Marsch has had a positive impact at the Yorkshire club since taking over from Marcelo Bielsa and goals from Raphinha, Rodrigo and Jack Harrison condemned the hosts to a ninth straight home defeat.
Leeds are in 16th place with 33 points. Watford are 19th with 22 points, six points from safety.
Photo: PHOTOSPORT Caption: Kai Havertz.