Chelsea edged past Southampton thanks to Marcos Alonso's winner to move level on points with second-placed Manchester United in the Premier League.
Alonso's long-range free-kick beat Saints goalkeeper Fraser Forster to put the hosts ahead in injury time of a first half the hosts had dominated.
Eden Hazard thought he had doubled the Blues' lead after the break, but Cesc Fabregas was flagged offside in the build-up.
Pedro hit the post and Fabregas shot wide as Southampton, now winless in five matches, rode their luck at Stamford Bridge.
It is an eighth win in 10 league games for Antonio Conte's side, who are 11 points adrift of leaders Manchester City alongside Manchester United.
However, United, who boast a better goal difference than Chelsea, face West Brom on Sunday.
Chelsea classy but not clinical
Conte said his expectation was "to suffer" before Saturday's game, but his side were in complete control throughout.
They should have been in front long before Alonso's speculative, curling free-kick from distance that caught Forster out low to his right.
Willian, Hazard and Pedro impressed with intricate passing and neat footwork - but with forward Hazard dropping off when marshalled by a deep-lying Southampton back five, Chelsea were lacking a cutting edge and focal point in the area.
Conte opted to keep striker Michy Batshuayi on the bench, while top scorer Alvaro Morata - who has been watching videos of club legend Didier Drogba's goals for the Blues - was only deemed fit enough to also sit among the substitutes.
Chelsea's club record signing was given the final 17 minutes to prove he was up to speed in an attempt to put the game beyond Southampton - and he very nearly did with a smart turn and strike soon after coming on.
The Spaniard combined with compatriot and fellow substitute Fabregas for the latter to force another save from Forster late on.
It was Fabregas who teed up Hazard for the Belgium forward's only shot on goal, which found the net but was ruled out for offside.
Blue Christmas for Saints?Charlie Austin had Southampton's only two shots on target after coming off the bench
Southampton are now without a win in five games since beating Everton in November, although during that run they have been narrowly beaten by runaway leaders Manchester City and conceded a late equaliser against Arsenal.
It was a much more disciplined performance than Wednesday's 4-1 drubbing by Leicester, and they frustrated champions Chelsea until the third minute of injury time in the first half.
Boss Mauricio Pellegrino made six changes, with defender Virgil van Dijk, long linked with a move away from the club, one of those to drop to the bench.
Charlie Austin - with two goals in three games prior to Saturday's defeat - was another to find himself left out, but it was the striker's arrival on the hour mark that seemed to offer Saints their most likely route back into the match.
He forced a save from Thibaut Courtois with his first touch and managed Southampton's only other shot on target, though Chelsea were never really troubled.
Southampton are now just three points above the relegation zone, with the visit of Huddersfield next Saturday taking on added importance before tricky trips to Tottenham on 26 December and Manchester United four days later.
Man of the match - Marcos Alonso (Chelsea)Marcos Alonso was Chelsea's most dangerous outlet.Repeatedly finding himself in attacking areas, the wing back scored the winner and had more shots on goal than any of his team-mates, three of which were on target.
'We needed a second goal to relax' - what they said
Chelsea boss Antonio Conte:"When you do not score the second goal, you have to suffer.You are afraid at every corner and free-kick and the opponent has the chance to draw.
"We dominated the game, shooting 24 times and hitting the post, and we needed to score the second goal to be relaxed.If you shoot only twice and score two goals, you must be worried.We had lots of shots but we must be more accurate in our finishing.
"In the past 10 games, we have won eight, drawn one and lost one.This is our run, you have to consider the last 10 games, not just two.It shows we are doing our job."Antonio Conte believes Chelsea 'dominated' the game
Southampton manager Mauricio Pellegrino:"It was a difficult game - especially in the second half we suffered a lot.When you play with five defenders, you do not have a lot of people in the middle and they managed the ball more.
"The quality of the goal was good, but maybe we can learn more from there.It is not easy to have many chances against Chelsea.We had three clear chances but could not score.
"The team is training well, the mentality is good and we are fighting.We are creating a good atmosphere to try and bounce back from this situation.Football is tight but we have another opportunity next Saturday."Chelsea 1-0 Southampton:Mauricio Pellegrino is pleased that his team competed til the end
Buy a ticket, win the raffle - the stats
- Alonso has had a hand in 14 goals for Chelsea (10 goals, four assists) - more than any other Premier League defender.
- Only striker Morata (49) has attempted more shots in the Premier League for Chelsea this season than Alonso (34).
- Chelsea have scored seven direct free-kicks under Conte in all competitions, more than any other Premier League side since the start of last season.
- Southampton have only won two of their 41 away top-flight matches against the reigning champions - they beat Leeds United in March 1970 and Chelsea in October 2015.
- Southampton have kept one clean sheet in their past 25 Premier League games against the Blues.
Chelsea host Bournemouth in the Carabao Cup quarter-finals on Wednesday (19:45 GMT kick-off), before visiting Everton in the Premier League next Saturday (12:30).
Southampton welcome Huddersfield in the league on 23 December (15:00)....