Even after the hosts had gone ahead through Shane Long's fine first-half goal, the Blues continued to play with confidence and became the first team to score against Southampton in seven games thanks to Cesc Fabregas' cross-cum-shot in the 75th minute.
Branislav Ivanovic's close-range 89th-minute header then secured a victory that likely ends seventh-placed Southampton's faint hopes of qualifying for next season's Champions League.
The result leaves Saints seven points behind the top four and Chelsea, in 11th, still in pursuit of the top 10, but the additional three points strengthens their sense of momentum in a season that may yet not prove so dreadful.
Enjoying a run of five wins from their past six fixtures, it was surprising that Southampton manager Ronald Koeman made changes to his team in replacing striker Graziano Pelle with Charlie Austin and recalling right-back Cedric for the unfortunate James Ward-Prowse.
Chelsea, as expected, remained unchanged from the team which last weekend defeated Manchester City 5-1 in the FA Cup
However, they were forced into a sixth-minute substitution when Pedro went down injured with Oscar his replacement
Their interim manager Guus Hiddink had overseen only one defeat and a significant improvement since his return to the club in December, but, by his own admission, their in-form hosts represented more than a routine threat.
It was in that context that Southampton created the more convincing of the first half chances.
Long headed just over the crossbar, with Thibaut Courtois out of position and most of the goal to aim at, from Virgil van Dijk's 10th-minute right-wing cross, and in the 31st minute Austin struck just wide of the right post when shooting from the edge of the area.
Chelsea, however, were also gradually improving, y et just as Eden Hazard shot high and wide after a nice build-up, an individual error led to Southampton taking the lead
With the softest of headers, Chelsea left-back Baba Rahman headed into Long's path in the 42nd minute, and the Ireland forward raced through on goal to demonstrate his composure with the classiest of deft, close-range chips over the onrushing Courtois and into the back of the net.
Fabregas had already criticised Rahman for conceding possession when misreading the Spaniard's pass, so it was perhaps little surprise when Hiddink replaced the left-back with Kenedy at half-time.
Chelsea sought an equaliser after the interval, hoping to finally breach Forster's goal, but Diego Costa volleyed wide of the left post from in front of goal from Hazard's superbly-delivered cross.
There was a touch of fortune about Fabregas' equaliser
The Spaniard appeared to be crossing to Hazard from the left of the area but the Belgian's sheer presence made Forster hesitate and watch the in-swinging delivery creep past him and inside his left post
Then Willian's run and shot from the edge of the area went just wide, which looked like Chelsea's best chance of victory had passed
But the Brazilian sent an 89th-minute corner to Ivanovic and the defender routinely headed the winning goal in from in front of goal to continue their fine form
TWEET OF THE MATCH
"Goal!!!! Captain marvel Ivanovic #mmlove #cfclive" - Former Chelsea defender Mario Melchiot enjoyed Ivanovic's winner
PLAYER RATINGS
SOUTHAMPTON
Fraser Forster: 6 (out of 10)
Cedric: 7
Virgin van Dijk: 7
Jose Fonte: 7
Ryan Bertrand: 7
Matt Targett: 6
Oriol Romeu: 6
Steven Davis: 7
Jordy Clasie: 6
Shane Long: 8
Charlie Austin: 7
Subs
Graziano Pelle: 6
James Ward-Prowse: 7
Sadio Mane: 6
CHELSEA
Thibaut Courtois: 6
Cesar Azpilicueta: 7
Branislav Ivanovic: 7
Gary Cahill: 7
Baba Rahman: 5
John Obi Mikel: 7
Cesc Fabregas: 8
Pedro: 5
Willian: 8
Eden Hazard: 8
Diego Costa: 7
Subs
Kenedy 6
Nemanja Matic: 5
Oscar: 8
STAR PLAYER
Willian - The one player not to have disappointed for Chelsea this season was again impressive
His energy, desire and ambition deserved a goal and contributed more to their performance than any other, even amid strong displays from team-mates operating in similar areas, Cesc Fabregas, Eden Hazard, Diego Costa and Oscar included
Provides so much balance to Chelsea's team, almost socred their winning goal and then delivered the cross from which Branislav Ivanovic actually did.
MOMENT OF THE MATCH
Mid-way through the second half, with Southampton leading Chelsea 1-0, Charlie Austin went down in the penalty area under a challenge from Gary Cahill
At the time it appeared he was simply pursuing a penalty, but replays suggested a spot-kick may have been justified and, at 1-0, would likely have secured victory for Southampton.
VIEW FROM THE BENCH
Guus Hiddink has transformed Chelsea since he succeeded Jose Mourinho, giving them a familiar resilient quality and ability to consistently earn results
Forget Antonio Conte or other managerial candidates, interim manager Hiddink would be the best man for the job, if only he wanted to stay
R onald Koeman deserves great credit for Southampton's recent form and the job he has done there since his appointment in the summer of 2014
He could do little about the fact his side were not awarded a penalty at 1-0 up, and the fact that Chelsea won largely because of their superior quality
Perhaps they could have pursued a second goal with greater intent, but there is little else he could be criticised for
MOAN OF THE MATCH
Baba Rahman looked out of his depth for Chelsea
Cesc Fabregas criticised him for costing possession in the first half, suggested his team-mates are already short of patience for him
That was before his misplaced header gifted Shane Long the chance from which Southampton took the lead, leading to his substitution at half-time
Who sanctioned his signing, for a reported £22million? And are they aware they sold Ryan Bertrand to Southampton for £10million, less than half of that.
WHO'S UP NEXT
Bournemouth v Southampton (March 1, Premier League)
Norwich v Chelsea (March 1, Premier League)
Source : PA
Source: PA