The best deal in the standings is achieved by the Mancunians, fifth one point behind Tottenham, but with one game more to play.
Their victory is all the more important as it comes after a turbulent international break, marked by the acrimonious departure of Cristiano Ronaldo and the sale of the club by the Glazer family.
The other good news was the entry tenure of French central defender Raphaël Varane, nine days after the World Cup final lost against Argentina.
Erik Ten Hag's players made the difference in the first half.
Marcus Rashford was first on the receiving end of a low corner kick by Eriksen (19th, 1-0), before Anthony Martial concluded a fine collective combination, just three minutes later, with Rashford for the serve (22nd, 2-0).
Fred scored late in the game on a pass from Casemiro (87th, 3-0).
With three next matches against teams within reach (Wolverhampton, Bournemouth and Everton), the Red Devils can rest easy.
Chelsea without forcing
At the start of the evening, Chelsea reassured themselves (2-0) against an uninspired Bournemouth formation, thanks to two goals from Kai Havertz (16th) and Mason Mount (24th).
Chelsea defender Marc Cucurella (in blue) during the English Premier League match against Bournemouth at Stamford Bridge stadium in London on December 27, 2022. © Ian Kington / AFP
A victory that allows him to take the second part of the championship by the right end: after a chaotic start to the season, saved by a qualification for the knockout stages of the Champions League, the Blues occupy only eighth place in the standings , 6 points behind fourth Tottenham.
Graham Potter's takeover of the team after Thomas Tuchel's ousting in mid-September had been successful with a month of good results, but the weeks leading up to the World Cup had been tricky for Chelsea, with three straight defeats in the league at Brighton (4-1), ahead of Arsenal (0-1) and Newcastle (2-0).
Graham Potter's players were also knocked out of the League Cup by Manchester City.
Despite plenty of chances against Bournemouth, Chelsea could not improve their goal difference and their attacking record, which remains one of the worst in the Premier League (19 goals in 15 matches).
But Graham Potter sees this victory as another step in the club's transition: "The first half was good, with a fantastic attitude. The players gave their best and deserved this victory."
The only bad news: the injury to Reece James, who was making his first appearance since October.
The right side limped out.
Continuation and end of this 17th day on Wednesday, with Leeds - Manchester City (9 p.m.), a crucial trip for Pep Guardiola's players who are eight points behind leader Arsenal.
© 2022 AFP