Liverpool stormed to the top of the table by tearing Manchester United to shreds in a 4-0 win at Anfield on Tuesday.
City were not so sparkling, but held their nerve to edge back one pont ahead in the title race thanks to second-half goals from Riyad Mahrez, Phil Foden and Bernardo Silva.
Mahrez was guilty of missing the best chances of a tense first 45 minutes for the English champions against a Brighton side that had won at Arsenal and Tottenham in their last two outings.
However, there was little doubt over the outcome once Mahrez bundled the ball home after Kevin De Bruyne’s burst opened up the visitors’ defence.
There was a hint of fortune about City’s second as Foden’s shot from a well-worked corner deflected past Robert Sanchez.
Silva then sealed the points with a sumptuous finish from De Bruyne’s lay-off.
– Gunners finally fire –
Arsenal were in pole position for a return to the Champions League until a run of three consecutive defeats.
But they moved level on points with fourth-placed Tottenham after a six-goal thriller.
Scoring goals has been a problem for Mikel Arteta’s men since the departure of Pierre-Emerick Aubameyang, but Eddie Nketiah took his chance with a rare start to score his first Premier League goals in over a year.
The all-time record goalscorer for England’s under-21s pounced on a huge error from Andreas Christensen to slot the opener past Edouard Mendy.
Chelsea took just four minutes to equalise as Timo Werner’s deflected shot caught Aaron Ramsdale napping at his near post.
Emile Smith Rowe put the Gunners back in front with a cool finish at the end of a glorious Arsenal move that started with Granit Xhaka dribbling out of his own box.
Again, though, Arsenal were pegged back as Cesar Azpilicueta steered home Mason Mount’s cross.
There was a reduced crowd at Stamford Bridge for the first time since restrictions placed on the club prevented them from selling tickets not purchased prior to UK government sanctions imposed on owner Roman Abramovich.
However, Arsenal were able to sell out the full away allocation and the visiting fans were jubilant when Nketiah took advantage of more shoddy Chelsea defending from Malang Sarr to put his side ahead for a third time.
Bukayo Saka then sealed the win with a stoppage-time penalty after he had been brought down by Azpilicueta.
At the bottom of the table, Everton snatched a much-needed point in their battle to beat the drop as Richarlison’s 92nd-minute strike earned a 1-1 draw against Leicester at Goodison Park.
The Foxes led for 87 minutes after Harvey Barnes’ early opener.
Everton edge four points clear of the relegation zone, but Burnley can cut that gap when they host Southampton on Thursday.
Newcastle were also fretting about relegation at the turn of the year, but the Magpies are up to 11th after a sixth consecutive home win.
Miguel Almiron scored the only goal at St. James’ Park to round off a disappointing week for Crystal Palace after their FA Cup semi-final exit to Chelsea.