The club's record signing produced an outrageous flicked finish at a vital point of the second half to restore Spurs' two-goal lead and help them clinch just their second Premier League win in seven.
The Blades had just got back into the game through David McGoldrick's header after first-half Serge Aurier and Harry Kane goals had put the visitors in command.
Spurs, who have thrown away 10 points from winning positions this season, might have been feeling nervy, but Ndombele came to rescue with his goal-of-the-season contender.
It helped Jose Mourinho's side, who left Dele Alli at home amid speculation surrounding his future, get some momentum ahead of their next league game in 10 days against Liverpool.
For Sheffield United it was their 16th defeat of the campaign and suggested Tuesday's first win of the season against Newcastle may have been a false dawn in terms of hopes of a great escape.
Additional reporting by PA.