The best opportunity of a cagey first half fell the way of the hosts, as Ismaila Coulibaly fired wide from a promising one-on-one situation.
Chances still proved to be few and far between in the second, but as the fifth-round tie headed towards extra time, Iliman Ndiaye's produced a 79th-minute winner to send his side through to the last eight of the FA Cup.
While Sheffield United can look forward to their third FA Cup quarter-final in four seasons, Tottenham will be left to mull over a fourth consecutive fifth-round exit in the competition.
The first FA Cup meeting between the two sides in 65 five years failed to come alive until the half-hour mark when Richarlison was sent through on goal.
As the Sheffield United defence appealed for offside, the Brazil international unleashed an attempt at goal, but he failed to keep his powerful effort on target.
Richarlison's countryman Lucas Moura had Wes Foderingham scrambling five minutes before half time, with his clipped cross bouncing off the top of the crossbar.
Despite threatening little in the opening 45, the Championship side were gifted the best chance of the first half when Pierre-Emile Højbjerg's weak header back to his goalkeeper was pounced on by Coulibaly, who subsequently lost his composure, slashing his effort wide of Fraser Forster's goal.
Foderingham had little to do in the first period, but the Sheffield United goalkeeper was required within three minutes of the restart, comfortably gathering a glancing Ivan Perisic header from a Son Heung-min corner.
The South Korea international then tried his luck from the edge of the area, but his wayward effort flew into the stand behind Foderingham's goal.
With Spurs still unable to find a way through a stubborn Sheffield United defence, captain Harry Kane was summoned from the bench in the 65th minute.
However, it was a Sheffield United substitute that produced the match-winning moment with just over 10 minutes remaining.
After collecting the ball in the penalty, Ndiaye's exquisite close control allows him to create the space to drive a low strike under Forster at the near post.
As Tottenham desperately searched for a late leveller, they managed to create one promising opportunity when Perisic's lofted cross found Kane, who was unable to direct his poor header on target, ensuring Sheffield United could celebrate an FA Cup upset.
Sheffield United will face Blackburn Rovers in the last eight, and ironically, they meet their fellow Championship side in the league on Saturday.
Tottenham, meanwhile, will have to pick themselves up for a Premier League away meeting with Wolverhampton Wanderers at the weekend.