Chelsea moved up to 11th after coming back from a goal down to beat Southampton courtesy of a Branislav Ivanovic header.
Shane Long headed high for the home side but atoned when he pounced on a Baba Rahman blunder before clipping a shot over keeper Thibaut Courtois.
Diego Costa volleyed wide for Chelsea but the visitors equalised when a Cesc Fabregas cross crept in.
Chelsea finished strongly and Ivanovic headed in from a Willian corner.
Hiddink comes out on top against Koeman
Chelsea manager Guus Hiddink managed Southampton counterpart Ronald Koeman when the pair won the European Cup with PSV Eindhoven in 1988.
They later fell out over Hiddnk’s appointment as Netherlands manager in 2014, although both have said there were no hard feelings.
They shared a handshake and a few words before their teams competed in a fascinating match.
Southampton were initially on top but Chelsea showed they had the greater stamina and capitalised on the home side dropping back too much after the break.
Hiddink will not only be pleased with his side’s desire and commitment but the fact they recovered from conceding against a team who had not let in a goal in six games.
The Blues remain unbeaten in the Dutchman’s 11 league games since he took over from Jose Mourinho.
Do Southampton have cause for complaint?
Southampton had been unbeaten in six league games, including five wins, before this match.
Keeper Fraser Forster set a top-flight league record of going 667 minutes without being beaten when the clock reached 34 minutes at St Mary’s and, when he did eventually let a goal in, it was in bizarre circumstances.
The assistant was flagging for a foul by Chelsea’s Kenedy on Cedric Soares but referee Martin Atkinson overruled and Fabregas sent in a low curling cross, which Forster misjudged as it went across him and in at the far post.
“I don’t understand that. The linesman is the closest to the situation. If it is a fault by Kenedy then you have to listen to the linesman. That’s why you have linesmen – to help you,” Koeman said.