The hosts needed a Marcos Alonso free kick in the dying stages of the first half to beat their out-of-form visitors and make it five consecutive Premier League home wins, closing the gap on leaders Manchester City to 11 points in the process.
Southampton, meanwhile, drop down to 12th having seen their winless run extend to five matches, with just three points now separating them from the relegation zone.
Chelsea boss Antonio Conte opted to leave fit-again top-scorer Alvaro Morata on the bench as he made just one change from the midweek win over Huddersfield Town, with captain Gary Cahill replacing Antonio Rudiger.
By contrast, Southampton made six changes from their demoralising 4-1 home defeat at the hands of Leicester City on Wednesday night, with the likes of Virgil van Dijk, Dusan Tadic and Charlie Austin among those to drop to the bench for the visitors.
Mauricio Pellegrino would have demanded a response to that midweek loss, and his team settled quickly in the capital. Indeed, the Saints were the first to threaten the opening goal of the contest when Ryan Bertrand's low cross took Thibaut Courtois out of the equation, but Cahill sorted his feet out in time to deal with the danger.
Chelsea were slow to settle into the match, but they almost opened the scoring 15 minutes in when Willian exchanged passes with Alonso before firing his finish a couple of yards wide of the target.
It took until the 21st minute for either side to have a shot on target when Cahill's long-range strike was kept out by Forster, and the Southampton keeper was called into action again shortly afterwards to palm N'Golo Kante's deflected shot away.
A crucial last-ditch challenge from Bertrand then denied Willian as Chelsea's pressure continued to grow before Forster was forced into another smart save at his near post by Alonso's snapshot from inside the penalty area.
Chelsea were denied by the woodwork in the closing stages of the first half after Pedro had bundled through a couple of challenges on his way into the box, eventually unleashing a shot which took a deflection on its way against the upright.
The hosts did go into half time with the lead, though, as Alonso broke the deadlock deep into first-half stoppage time with a perfectly-placed free kick which nestled into the bottom corner after Forster was slow to react.
Chelsea picked up where they left off at the start of the second half, although they were largely limited to long-range strikes in the opening exchanges as Willian and Cesar Azpilicueta fired efforts well off target.
Pellegrino turned to Austin off the bench in place of the ineffective Manolo Gabbiadini, and the change almost produced an instant reward when Austin was played through on goal by Pierre-Emile Hojbjerg only to put his finish too close to Courtois.
It served as a warning shot to Chelsea, who had hitherto been coasting at 1-0, and they thought they had built a two-goal cushion shortly afterwards when Eden Hazard fired a clinical finish into the bottom corner, only to be denied by the offside flag after a smart one-two with Cesc Fabregas.
Conte's side continued to push for that second goal, though, and Alonso stung the palms of Forster with another long-range strike before Morata was introduced and quickly became involved in the action when he was denied from a tight angle.
At just one goal down Southampton still had a glimmer of hope, and Austin again threatened an equaliser moments later when he drew another stop from Courtois.
Chelsea were soon back on the front foot, though, and Fabregas was agonisingly close to putting the game beyond their visitors once and for all when he poked the ball past Forster from an impossible angle, only to see it roll across the line and ultimately to safety.
The Saints refused to give up without a fight and again came close to an equaliser with just five minutes remaining when Austin darted to the near post, but he could not steer Jack Stephens's low cross on target.
Despite their lead it was Chelsea who looked most likely to add the game's second goal in the closing stages, with Azpilicueta and Fabregas both drawing saves from Forster in stoppage time before the referee brought an end to the game.
The win sees the champions move level with second-placed United - at least until the Red Devils face West Bromwich Albion on Sunday - and, even more importantly, it opens up a six-point gap to fifth-placed Burnley after they were held by Brighton & Hove Albion.
Southampton, meanwhile, still face matches against Tottenham Hotspur and United before the end of the year and, with only three points separating them from the relegation zone, may need a result in one of those games to keep them away from the bottom three.
Chelsea (3-4-3): Courtois; Azpilicueta, Christensen, Cahill; Moses (Zappacosta, 82'), Kante, Bakayoko, Alonso; Willian, Hazard (Morata, 73'), Pedro (Fabregas, 68')
Southampton (3-4-3): Forster; Stephens, Yoshida, Hoedt; Cedric (Lemina, 17'), Romeu, Hojbjerg (Boufal, 72'), Bertrand; Ward-Prowse, Gabbiadini (Austin, 61'), Redmond