The hosts took the lead against the run of play in the first half when Nathan Redmond played a brilliant ball to send Takumi Minamino clear and the on-loan Liverpool striker showed great composure to slot beyond Edouard Mendy.
But the Saints gifted Chelsea an equaliser eight minutes after the break when Danny Ings brought down Mason Mount inside the box and the Blues midfielder stepped up to send Alex McCarthy the wrong way from the penalty spot.
Chelsea were unable to kick on after that and instead it was Southampton who went closest to grabbing a winner as Jannik Vestergaard hit the crossbar with a header before Ings put the loose ball into the side-netting.
Need a VPN? Or seeking to switch? Then support Tribal Football by clicking here to sign up with our official partners NordVPN. Not only will you receive the best VPN experience, but also great discounts by signing up via Tribal Football. Thanks for your support!