Burnley took the lead minutes later through Sam Vokes after a cross from the right from Matt Lowton.
And though Alvaro Morata and David Luiz would net in the second half to spare Chelsea some embarrassment, Cesc Fabregas' late second booking further reduced their chances of completing an improbable comeback.
Egyptian defender Ahmed Hegazi scored a first-half header on his Premier League debut to give West Bromwich Albion a well-deserved 1-0 victory over Bournemouth at the Hawthorns on the opening day of their season.
Chelsea were already without the likes of Eden Hazard, Victor Moses and Pedro as they began their title defence at home to Burnley on Saturday afternoon.
Spanish worldwide Alvaro Morata came from the bench to score the first goal for the Blues in the 69th minutes before David Luiz netted at the death as the match ended 3-2 in favor of Burnley.
Southampton had 29 shots on goal, with Manolo Gabbiadini and Dusan Tadic wasting the best of the chances. A smart and enthusiastic runner, the Spaniard provided an immediate upgrade on the anonymous Michy Batshuayi and even marked his thankless cameo with an impressive goal, ghosting in at the back post to nod in Willian's inviting cross, before flicking on for Luiz to score.
But Liverpool came out fighting after the break, and grabbed an equaliser 10 minutes into the second half after Watford keeper Heurelho Gomes brought down Mohamed Salah in the area.
Burnley FC's Ben Mee (C) looking forward to leave Stamford Bridge with surprise win over Chelsea.
Chelsea are the league's best team when it comes to opening the season.
"That's a huge result - a lot was made of our away form last season".