(AFP/Ian Kington)
Samir Nasri had given City a fifth-minute lead at White Hart Lane, but Clint Dempsey equalised with 15 minutes to play before substitute Jermain Defoe and Gareth Bale netted to complete a rousing comeback.
As well as revitalising Spurs' hopes of Champions League qualification, the result means that United can secure a 20th league crown if they win at home to Aston Villa on Monday.
"We had everything in order. It is strange. It is not a correct result, but congratulations to Tottenham for the win," City manager Roberto Mancini told Sky Sports.
"The championship was finished three or four weeks ago. Manchester United deserved to win.
"I think it is important to win as many of our five remaining games, and win the FA Cup final."
Spurs' victory left Andre Villas-Boas' side level on 61 points with Chelsea, who occupy the fourth and final Champions League berth, and two points below third-place Arsenal with a game in hand.
Chelsea are in action later on Sunday when interim manager Rafael Benitez returns to former club Liverpool for the first time.
"The gaffer (manager) told me to move out wide and it worked out well. Our opening goal gave us and the crowd belief," said Bale.
"We showed our character. The club is moving forward every year. The players want to play in the Champions League, and we showed that today."
Tottenham recalled Bale after an ankle injury and the hosts started the game in positive fashion, but it was City who drew first blood.
Carlos Tevez's deft pass released James Milner and from the Englishman's cross, Nasri steered a volley past the lunge of defender Kyle Walker on the Spurs goal-line.
City goalkeeper Joe Hart had to spread himself to prevent Walker from equalising, but City continued to carry a threat in attack.
Nasri poked the ball wide after being freed by an adroit cushioned pass from Tevez, who then drew a reflex save from Spurs goalkeeper Hugo Lloris with a close-range header.
Dempsey headed over for Spurs shortly before half-time, but the American was in the right place to tap home in the 75th minute after Bale threaded a glorious cross into the box with the outside of his left foot.
Defoe put Spurs ahead four minutes later, jinking inside Vincent Kompany and lashing a shot into the bottom-right corner, before Bale added a third with a cool, chipped finish in the 82nd minute.
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