Southampton substitute Michael Obafemi’s 96th-minute equaliser prevented Manchester United from jumping up to third place and leaves their Champions League qualification still in the balance.
The Saints started off well at Old Trafford and went ahead through Stuart Armstrong’s 12th-minute strike, following Paul Pogba’s mistake.
But United responded immediately – Marcus Rashford slotting home the equaliser before Anthony Martial fired a superb second three minutes later.
Obafemi then bundled it in at the back post from a set-piece deep in stoppage time after it had been flicked on by Jan Bednarek – leaving United fifth with three games left.
Man Utd XI: Matic, De Gea, Lindelof, Pogba, Maguire, Shaw, Martial, Bruno Fernandes, Rashford, Wan-Bissaka, Greenwood
Subs: Romero, Mata, Ighalo, Fred, Pereira, Bailly, Daniel James, McTominay, Brandon Williams
Southampton XI: Bertrand, McCarthy, Romeu, Armstrong, Ings, Redmond, Stephens, Ward-Prowse, Bednarek, Adams, Walker-Peters
Subs: Shane Long, Vestergaard, Hojbjerg, Gunn, Danso, Vokins, W. Smallbone, Obafemi, W. Ferry