French teenager Anthony Martial, having scored as a substitute on his Premier League debut in Manchester United's last game, added two more goals to earn his team a 3-2 win at Southampton.
The victory took Louis van Gaal's side into second place, two points behind neighbours Manchester City.
Graziano Pelle put Southampton ahead in the 13th minute but Martial, who cost $56.4m from AS Monaco on the last day of the transfer window, equalised 10 minutes before halftime.
His second goal followed a dreadful backpass by Southampton's Japanese defender Maya Yoshida.
Juan Mata added United's third midway through the second half before Pelle gave his team late hope by heading in Sadio Mane's cross.
Elsewhere, Danny Ings scored his first Liverpool goal within three minutes of coming on as a substitute but promoted Norwich City fought back to draw 1-1 at Anfield.
The home side had started the game in the bottom six following Tottenham Hotspur's win earlier on Sunday and the point lifted them two places to 13th, two places behind Norwich and level on eight points with their opponents.
Liverpool, with their England striker Daniel Sturridge back for the first time since April, brought on Ings for Christian Benteke at halftime and the former Burnley man scored a fine goal almost immediately.
But Norwich central defender Russell Martin equalised with his third goal of the season after a mistake by Liverpool goalkeeper Simon Mignolet.
Tottenham 1-0 Crystal Palace
Liverpool 1-1 Norwich
Southampton 2-3 Manchester United