It looked like Robin van Persie's header in the first half was going to take the spoils for United with David De Gea producing a string of fine saves to deny Jermain Defoe, Gareth Bale, Aaron Lennon and, most notably, point-blank from Dempsey in the second half.
But the USA striker, who hit the winner in our famous win at Old Trafford in September, had the final word in the 93rd minute.
Benoit Assou-Ekotto crossed from the left, Steven Caulker went up with De Gea, the ball fell to Aaron Lennon, he fired across goal and Dempsey was there to turn the ball home from six yards.
It was no less than we deserved after dominating the second half - 23 shots to United's six underlining our territorial advantage.
Andre Villas-Boas made three changes to the team that started at QPR last weekend.
Caulker came back into central defence for Jan Vertonghen, Parker replaced injured Sandro and Dempsey came in for Emmanuel Adebayor.
We didn't get going in a somewhat flat first half.
Having said that, we still forced De Gea ito the only two serious saves of the half from Defoe and Bale.
Parker, everywhere in that opening period, had the first effort of note, a curler wide from 20 yards before van Persie guided Phil Jones' cross into Hugo Lloris' hands.
De Gea made a routine save down to his left from Lennon before the opening goal on 25 minutes, van Persie unmarked at the far post to head home Tom Cleverley's cross.
We responded immediately as Defoe almost caught De Gea out at the near post, the goalkeeper reacting quickly to make a smart save.
Bale came closest to equalising just before the break when Rafael headed out Lennon's cross to the Welsh star, who fired back through a crowded box but De Gea was there to block with his legs.
We turned up the heat in the freezing temperature at the start of the second half.
There was only 45 seconds on the clock when Lennon released Defoe in the inside right channel, he had to take his shot quickly as Ferdinand and Nemanja Vidic closed in, but fired wide.
Dembele did well to block from Danny Welbeck before Bale curled just over from 20 yards and then the best chance - and save - of the half as Dembele wriggled away from two men on the egde of the box and found Dempsey, he rode Patrice Evra's challenge and poked at goal from six yards, only to see De Gea touch the ball wide with his right knee.
We continued to press. Bale's cross from the left somehow evaded Dempsey and Defoe sliding in and De Gea was there again to touch Dempsey's effort wide after Defoe's shot was blocked by Ferdinand.
United remained dangerous on the break - Welbeck just failed to turn Rafael's cross on target - but momentum remained in our favour as Lennon released Defoe only for Ferdinand to make a sliding block as he pulled the trigger with 12 minutes left.
Defoe then fired straight at De Gea and Bale's shot from the edge of the box deflected off Ferdinand and fizzed inches wide with the goalkeeper rooted to the spot.
We finally gained our reward as final seconds ticked on three minutes added time. De Gea struggled to punch clear Assou-Ekotto's cross, Lennon fired across goal and Dempsey was there to plant the ball home, sparking joyous scenes from all home fans.
Spurs (4-2-2): Lloris; Walker, Caulker, Dawson, Naughton (Assou-Ekotto, 65); Lennon,Dembele, Parker (Huddlestone, 80), Bale; Defoe, Dempsey. Unused subs: Friedel, Vertonghen, Livermore, Sigurdsson, Townsend.
Manchester United (4-3-3): De Gea; Rafael Da Silva, Ferdinand, Vidic, Evra; Jones, Carrick, Cleverley (Valencia, 75); Welbeck, van Persie, Kagawa (Rooney, 62). Unused subs: Lindergaard, Anderson, Giggs, Smalling, Chicharito.
Yellow cards: Spurs - Dawson. United - Carrick, Evra, Rafael, Rooney.
Goals: Spurs - Dempsey (90+3). United - van Persie (25).
Referee: Mr C Foy.