Southampton clawed their way back into the game twice to force the draw.
The game saw summer signing Hakim Ziyech make his debut for Chelsea while Christian Pulisic also featured for the first time for the Blues this season.
German forward Timo Werner scored his first Premier League goals after bagging a brace for the home side.
A win for Chelsea would have moved them up to second place and are now sixth on eight points.
GOAL Chelsea 1-0 Southampton (15 mins)
Werner had his first Premier League goal on 15 minutes after Ben Chilwell found him with a through ball and he worked his way through the Saints defence went past a couple of defenders before then lashing home.
In the 28th minute Werner scored again as he nicked in behind and coolly headed in from Jorginho’s ball over the top.
With two minutes left in the first half Danny Ings pulled one back for the visitors, turning in from Che Adams’ through ball.
Southampton were levelled on 57 minutes following Che Adams’ quick reaction to confusion at the back from Chelsea and proded in to score.
In the 59th minute Chelsea restored their lead thanks to Kai Havertz who tapped home Werner’s cross for his first league goal.
But two minutes into added time Vestergaard glanced in after Theo Walcott took aim to make it 3-3.
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