Chris Wilder’s side took the lead through Sander Berge’s first half strike at Bramall Lane.
But Tottenham were denied an equaliser moments later when Harry Kane’s goal was chalked off by VAR for a dubious handball against Lucas Moura.
Lucas appeared to have the ball kicked against his arm in the build-up to Kane’s strike and Tottenham manager Jose Mourinho complained angrily on the touchline.
Lys Mousset and Oli McBurnie rubbed salt into Mourinho’s wounds as they both netted for United after the interval.
Kane’s last minute goal was no consolation for Tottenham, who are now in grave danger of missing out on next season’s Champions League.
They sit nine points behind fourth placed Chelsea and seven adrift of fifth placed Manchester United after their first defeat since the restart.
The Blades, winners for the first time in five games following the hiatus, moved two points above Tottenham into seventh place, keeping alive their hopes of qualifying for European action.
United had not managed more than one shot on target in any of their previous three Premier League matches, going without a goal on each occasion.
It took less than 60 seconds for George Baldock to get an effort on target, but Tottenham keeper Hugo Lloris dived to his left to make the save.