United were rocked by Callum Wilson's opener after a slow start, but they took control of the game and sealed a deserved 2-1 victory thanks to Billy Sharp's equaliser, and a calm, late winner from substitute John Lundstram.
The result moved the Blades up to fifth in the Premier League table - within two points of Chelsea, who occupy the final Champions League spot.
Chelsea and Spurs, who are a place behind United, both have a game in hand on Wilder's men - and also both have to visit Bramall Lane, on April 25 and April 4 respectively.
And Wilder, who has taken his side to Dubai for their winter break ahead of their next game against Brighton and Hove Albion on February 22, said: "It was a great 70-minute performance.
"I wasn't impressed by the first 20, they dictated the pace of the game and went in front and deservedly so.
"But our reaction was good. My players showed the character they possess, they didn't feel sorry for themselves and created pressure and momentum and the supporters drove us on and lifted the players.
"To turn a losing position into a winning one shows what my group of players are about. We found a way to win. It was a great comeback. The belief the boys have is amazing."