Huddersfield Town boosted their Premier League survival hopes with a dramatic victory over Watford FC at the John Smith's Stadium.
Tom Ince scored the winner in injury time to see the Terriers claim just a third league victory in their last 16 games.
The Saints had looked to be taking advantage of kicking off before their relegation rivals, leading Chelsea 2-0 before capitulating to concede three goals in eight minutes to lose 3-2.
Olivier Giroud came off the bench to inspire the comeback, scoring either side of an Eden Hazard equaliser after Dusan Tadic and Jan Bednarek had struck for Southampton.
Meanwhile, Wilfried Zaha inspired Crystal Palace to a 3-2 victory over derby rivals Brighton & Hove Albion at Selhurst Park, the Ivory Coast winger netting twice in an entertaining first half which saw all five goals scored.
Roy Hodgson's side were two goals to the good with just 14 minutes played as James Tomkins drilled in his third of the campaign.
That lead did not last long, with Glenn Murray scoring from point-blank range against his former club to bring the Seagulls back into the contest.
Zaha restored the two-goal advantage with a bullet header from Luka Milivojevic's perfect cross and, in a frenetic opening 45 minutes, Jose Izquierdo struck with a fine finish for the visitors.
Town and Palace's wins meant Swansea City drop to 17th despite taking a point from Everton, with Jordan Ayew's second-half goal enough to earn the Swans a deserved share of the spoils after Kyle Naughton's unfortunate own goal had seen them fall behind.
In the other afternoon kick-offs, Burnley's run to the Europa League continued with a 2-1 win over Leicester City and a Mo Salah-inspired Liverpool ran out comfortable 3-0 winners over AFC Bournemouth at Anfield.
The final game of the day saw Manchester City move a step closer to securing the title with a 3-1 win at Tottenham Hotspur - Gabriel Jesus, Ilkay Gundogan and Raheem Sterling on target for Pep Guardiola's men.