Unlikely goalscorer Serge Aurier rose highest in the 5th minute at a corner to head Spurs into the lead, before Harry Kane doubled the scoreline with a fantastic bending effort from the edge of the area.
David McGoldrick did pull one back for the Blades with a fantastic header, but the goal proved to be nothing more than a consolation as Ndombele pulled off an incredible no-look outside of the foot lob to give his side all three points.
Story of the game
From the resulting corner taken by Son, Aurier managed to out-jump Bogle and head home to give Spurs the lead inside five minutes.
Kane not long afterwards played a one-two with Ndombele, giving the Englishman space to thread through a neat ball for Son to chase, but the Korean star's chip attempt struck the outside of the post, much to Ramsdale's relief.
Burke got the Blades' first real chance of the game after McGoldrick found him, his pace took him through on goal but from an acute angle - where his attempt was deflected wide for a corner.
Burke had another half chance about fifteen minutes later as Spurs began to sit off, as he found a yard of space to get a strike in from distance, forcing Lloris into making a good save down low.
It was Spurs however that scored the second goal of the game, and it came in the 40th minute when some high intensity pressing led by Son caused the turnover in possession deep in the Blades' half, giving the chance for Hojbjerg to slip in Kane who bent his shot past Ramsdale from just outside the area.
Sheffield United did start well in the second half, forcing a block out of Ndombele after a good build-up, before McGoldrick fired a shot well over.
Their better mentality in the second half was rewarded just under 15 minutes into the second half, when Fleck's wonderful cross was met by McGoldrick who powered his header past Lloris to give the Blades hope for getting something out of the game.
But just moments later, Ndombele hit back for Spurs with a stupendous chip with the outside of his boot, with his back to goal - an absolutely incredible goal from an incredible player to put his side back in the driving seat.
The goal only ushered the visitors into creating more chances, with Kane and Bergwijn both having attempts before Son cut inside and unleashed a goal-bound strike, which was deflected behind for a corner.
As the time for Sheffield United to try and claw their way back into the game dwindled out, Kane was presented an opportunity in added time to go equal with Bobby Smith in Spurs' all time top scorers on 207, but he leant back a little too much after Son laid the ball of him and saw his strike fly well over.
Man of the match - Tanguy Ndombele
It's difficult to remember the time when Mourinho was criticising the Frenchman for his lack of effort, because currently Ndombele is up there with the best midfielders on the planet - and today showed exactly why.
Anyone would be stupid to say that the 24-year-old isn't one of the most electrifying players right now - but it's the dirty work he's adding to his game that is benefitting Spurs even more - winning possession back six times and also coming out on top in six of his eight duels.
What a player Spurs have on their hands.