Goals from Serge Aurier, Harry Kane and Tanguy Ndombele has taken Jose Mourinho’s side to fourth on the Premier League table with 33 points.
The visitors had their tails up in the opening five minutes of the game when full-back Aurier rose highest to meet Heung-Min Son’s corner.
Spurs could have swiftly gotten their second goal two minutes later after Kane’s through ball found Son, who dinked the ball over the advancing Aaron Ramsdale but the South Korean’s effort clipped the outside of the post.
The intensity of the game dropped a little bit but the North Londoners had their second goal five minutes before the interval following a loose play from the Blades at the back as midfielder Pierre-Emile Hojbjerg robbed the ball from John Fleck, before he fed it to Kane, who turned away from Chris Basham before slotting into the bottom corner from the edge of the area.
Sheffield United found a glimmer of hope after the break when Fleck whipped an excellent ball in from the left which David McGoldrick popped up over the shoulder of Joe Rodon and glanced an excellent header into the bottom corner past the rooted Hugo Lloris on the 59th minute mark.
Tottenham restored their two-goal cushion to extinguish the hosts’ hopes for a comeback kind courtesy of Ndombele’s stunning effort three minutes later.
Spurs have registered their first away league victory against Sheffield United since December 1975, ending a seven-game winless run at Bramall Lane.
Tottenham return to action against Wycombe in the FA Cup fourth round on January 25 before entertaining Liverpool in the Premier League three days later while Sheffield United will be facing Plymouth Argyle in the FA Cup on Saturday.