The Blues came into this game in good form, winning five games in all competitions. The hosts, meanwhile, had won just one in their last six.
In a one-sided affair, Chelsea controlled proceedings in the early stages but failed to take the initiative and open the scoring.
The deadlock was instead broken by Southampton in the 33rd minute. A brilliant defence-splitting pass from Nathan Redmond was met by Liverpool loanee Takumi Minamino, who showed great composure to beat Edouard Mendy.
Chelsea pushed for an equaliser but ended the half trailing by a goal. The visitors came into the second half with guns blazing, winning a penalty after Mason Mount was felled by Southampton striker Danny Ings.
The 22-year-old promptly stepped up and fired home his fourth goal of the season and his second in three games.
Chelsea threw men forward in search of a winner, but that was not to be, as Southampton held on for a point.
The result means Chelsea could drop out of the top four if West Ham United grab a win, or Liverpool defeat Everton by four or more goals. Meanwhile, Southampton have moved up to 13th in the Premier League league table, leapfrogging Crystal Palace.
On that note, let's have a look at the Chelsea player ratings.
Edouard Mendy 6/10
The Chelsea shot-stopper was largely undisturbed by the toothless Southampton attack. However, the one time he was called to action, Edouard Mendy failed to keep out Takumi Minamino’s dinking shot.
Cesar Azpilicueta 6/10
The Chelsea captain manned the right side of Chelsea's three-man defence with aplomb, doing well to keep Danny Ings quiet all game.
However, there was nothing Cesar Azpilicueta could have done about Southampton's opener, as Nathan Redmond’s defence-splitting pass caught Kurt Zouma off guard. Nevertheless, the Spaniard showed great determination to track down the Liverpool loanee, but his last-ditch effort proved futile.
Kurt Zouma 5.5/10
The Frenchman made his first appearance in the Chelsea starting XI under new boss Thomas Tuchel.
However, Kurt Zouma failed to impress, as his lapse in concentration allowed Minamino through on goal and open the scoring for the hosts. The towering centre-back grew into the game in the second half, winning several aerial duels to keep his side in the game, though.
Antonio Rudiger 6/10
The former Chelsea outcast has turned a corner since the appointment of Thomas Tuchel. Antonio Rudiger was diligent in his defensive duties despite facing few threats from Southampton.
Rudiger almost cost Chelsea a goal in the second half when his sloppy pass led to a Southampton attack, but that eventually came to nothing.
Reece James 6.5/10
The Chelsea academy graduate continues to find his stride under the new Chelsea boss but struggled to impact the game significantly.
Reece James had little to do in defence as he tried to link up with his attacking colleagues. He made several darting runs forward but did cost Chelsea the three points when he missed a sitter in the closing stages of the game.
N'Golo Kante 7/10
N'Golo Kante was Chelsea's star performer against Southampton.
The Frenchman’s high energy level allowed him to cover lots of ground for the visitors, and he was on hand to stop Southampton attacks too. His quick passing and defensive cover in midfield allowed Chelsea to venture forward and look for the all-important winner.
Mateo Kovacic 6/10
The ex-Real Madrid man started off brilliantly, not putting a foot wrong to beat the Southampton press. However, Mateo Kovacic fizzled out in the second half and was hooked off for Jorginho with 14 minutes on the clock.
Marcos Alonso 6/10
Marcos Alonso once again played as a wing-back in Tuchel’s back-three system, which allowed him to move into advanced areas of the pitch. However, he was often caught out by the hosts' defensive positioning.
The Chelsea man was quiet all game. Alonso even missed a chance to get on the scoresheet in the first half when he fired a volley wide off the goal.
Mason Mount 7.5/10
Mason Mount was one of the bright sparks in a lethargic Chelsea display. The Chelsea academy graduate was full of energy all game, as he looked to threaten the Southampton defence.
His quick feet and superb movement earned Chelsea a penalty shortly after the second half.
With Jorginho on the bench, the midfielder converted the penalty to restore parity for his side.
Timo Werner 5/10
Despite getting into brilliant positions and finding pockets of space with his blistering speed, the German international failed to lay a foothold on the game. Timo Werner was wasteful on the ball and lacked threat going forward, finishing the game without a single shot on target.
Tammy Abraham 5/10
The Chelsea forward was a surprise inclusion in the Chelsea starting XI, considering he hobbled off with an ankle injury against Newcastle United.
However, Tammy Abraham struggled to get into gear as he looked off the pace the entire time he was on the pitch. His afternoon was riddled with several wayward passes before he was hooked off at the half-time break.
Player ratings of Chelsea substitutes
Callum Hudson-Odoi 4/10
With Chelsea going back to a four-man defence, Callum Hudson-Odoi was brought on for the misfiring Tammy Abraham. However, he struggled to sync with his Chelsea teammates and was shockingly substituted after barely 15 minutes.
Hakim Ziyech 3/10
Hakim Ziyech failed to influence the game to the extent Tuchel would have wanted. He made only 11 touches in his 15 minutes on the pitch, completing three passes while losing possession six times.
With Chelsea desperately searching for a winner, the Italian was brought on to spark new life in midfield. He had a decent 15-minute cameo but failed to influence the game’s result.