Under-pressure Arsenal manager Mikel Arteta’s troubles looked to have increased with several regulars ruled out for the visit of a Chelsea side that could have gone second with a win.
But the Gunners took the lead in the 35th minute through an Alexandre Lacazette penalty after Kieran Tierney was adjudged to have been clipped in the box by Reece James.
Nine minutes later, Granit Xhaka fired an unstoppable free kick over the wall and beyond the diving Chelsea keeper Edouard Mendy.
A visibly frustrated Chelsea coach Frank Lampard tried to turn the tide at half-time when he replaced out-of-form Germany striker Timo Werner with winger Callum Hudson-Odoi and Mateo Kovacic with Jorginho.
But Chelsea still could not get into gear and Arsenal sealed the win in the 56th minute when Saka floated what looked like a cross over Mendy and the ball hit the far post and went in.
Chelsea scored a consolation goal with five minutes to go when Tammy Abraham converted a cross by Hudson-Odoi and could have scared Arsenal further if Jorginho had not had a soft penalty saved by Bernd Leno.
Marcus Rashford put United ahead in the 23rd minute with a cool finish after being slipped in by Bruno Fernandes before Harvey Barnes equalised eight minutes later with a fine shot from the edge of the box.
Fernandes restored United’s lead in the 79th minute, drilling into the bottom corner after being found inside the area by substitute Edinson Cavani.
Again though, the lead was short-lived as Vardy’s first time shot on the half-turn from a low cross from Ayoze Perez, deflected off United defender Axel Tuanzebe and earned a point for the Foxes.
Aston Villa made light of playing half the match with 10 men to thrash Crystal Palace 3-0.
Bertrand Traore put an impressive Villa side ahead early on but the hosts had Tyrone Mings dismissed shortly before the break after picking up a second yellow card.
It made little difference as they outplayed Palace in the second half with Kortney Hause heading in from close range to double their lead in the 66th minute.
Anwar El Ghazi’s rasping finish 10 minutes later wrapped up the points for Villa and they could have won by a bigger margin had Ollie Watkins not been denied by the post late on.
Southampton were left frustrated by the woodwork and a disallowed goal as they were held to a 0-0 draw against Fulham at Craven Cottage.
After James Ward-Prowse hit the woodwork with a 26th minute freekick, Shane Long and Theo Walcott both had efforts disallowed for the Saints.
Fulham remain the relegation zone, on 11 points in 18th place, while Southampton are eighth on 25 points.
Manchester City secured a routine 2-0 win over Newcastle thanks to goals from Ilkay Gundogan and Ferran Torres to climb to fifth place.
Gundogan tucked home a cutback from Raheem Sterling to score in consecutive home games in the league and put City ahead in the 14th minute.
Torres, a winger, was playing as the lone striker in the absence of Gabriel Jesus — who has contracted the coronavirus — and scored for the second time in the league this season to make it 2-0. He showed a striker’s instinct to hold back as Federico Fernandez blocked a cross from the right and the ball arrived at the feet of Torres, who stroked in a finish from eight meters in the 55th.
Meanwhile, Everton moved two places up to second and finished in the top four during the Christmas holiday period for the first time in 16 years after a late Gylfi Sigurdsson goal gave them a 1-0 win at bottom team Sheffield United.
The result left Everton on 29 points from 15 games, while the winless Blades stayed rooted to the bottom with two points.