Romelu Lukaku took off his shirt to celebrate scoring a late winning goal in a memorable game at Old Trafford that swung one way and the other.
Three of the five goals on display were outstanding as United boosted their top-four prospects and leave Southampton just a point above the relegation zone.
The visitors took an unexpected lead before half-time when Yan Valery struck from long range strike for his first senior goal.
Romelu Lukaku was the hero of the hour at Old Trafford, popping up in the dying moments to score his second and win the tie
The forward instantly sprinted away and ripped off his shirt while celebrating with the Manchester United supporters
Lukaku's team-mates quickly piled on top of him, as the referee brandished a yellow card for the topless antics
In a game of stunning goals, James Ward-Prowse made it 2-2 after expertly curling home a free-kick from long range
The set piece specialist got the ball up and over the wall, leaving goalkeeper David De Gea unable to see until the last minute
The Spanish stopper was at full strength but couldn't get a touch to the ball as it made its way into the top corner
United fans could only watch on as the ball rattled past the sprawling De Gea and into the back of the net to level the score
But United fought back early in the second half when Andreas Pereira fired a cracker for his first United goal since 2015 before setting up Lukaku to give United the lead.
James Ward-Prowse levelled with 15 minutes left with a terrific free-kick but Ole Gunnar Solskjaer’s men staged a late rally with Lukaku scoring his second goal of the afternoon after 88 minutes.
Paul Pogba was then denied an injury-time penalty when his stuttering run-up failed to fool Angus Gunn in Southampton’s goal.
United made a fast start with Lukaku – who had scored twice at Crystal Palace on Wednesday - twice denied by excellent stops from Gunn.
Manchester United: De Gea; Young, Smalling, Lindelof, Shaw, McTominay, Andreas Pereira, Pogba; Rashford, Lukaku, Sanchez (Dalot 52')
Subs not used: Bailly, Grant, Rojo, Fred, Chong, Gomes
Booked:
Goals: Pereira 53, Lukaku 59, 88,
Manager: Ole Gunnar Solskjaer
Southampton: Gunn, Bednarek, Yoshida, Vestergaard, Valery, Ward-Prowse, Romeu, Hojbjerg, Bertrand, Redmond, Austin (Armstrong 63')
Subs not used: McCarthy, Stephens, Elyounoussi, Gallagher, Targett, Slattery
Booked: Bertrand
Goals: Valery 26, Ward-Prowse 75
Manager: Raplh Hasenhuttl
Referee: Stuart Attwell
Att: 74,459
MOTM:
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But after the visitors had a penalty claim turned down for Chris Smalling’s tug on Ryan Bertrand, their manager Ralph Hasenhuttl was able to punch the air with glee after 26 minutes.
Charlie Austin released Valery down the right and then dashed into the penalty area expecting a return ball. Instead, the 20-year-old Frenchman pulled the trigger from 25 yards with such power that a diving David de Gea could only succeed in pushing the ball into the roof of the net.
The partnership between Lukaku and Marcus Rashford took time to develop. At