Samir Nasri opened the scoring in the fifth minute and City held their lead until deep into the second half, but a three-goal blitz turned the game on its head.
Clint Dempsey netted the equaliser in the 75th minute and substitute Jermain Defoe quickly made it 2-1.
Gareth Bale sealed the victory on his return from injury after 82 minutes as Spurs closed the gap on London rivals Arsenal and Chelsea, and presented Manchester United with the chance to win the title if they can beat Aston Villa on Monday.
City made the early breakthrough after just five minutes as Nasri steered a well-controlled shot past Hugo Lloris and covering defender Kyle Walker from James Milner's cut-back, after terrific work by Carlos Tevez down the right wing.
Nasri nearly went from hero to villain minutes later as he mistimed a challenge on Walker and caught the Tottenham right-back on the shin with a high boot, but he escaped punishment.
Spurs carved out a couple of chances to equalise before the interval without ever really enjoying a sustained period of pressure, with Bale initially a peripheral figure and the main threat coming from Walker, who had a shot well saved from a tight angle by Joe Hart.
Dempsey also powered a header off target, but City continued to look lively in attack and nearly added to their lead when Nasri poked a shot wide and Edin Dzeko had a shot well held down to his right by a diving Lloris.
Benoit Assou-Ekotto was lucky to stay on the pitch early in the second half after a mistimed rash challenge on Pablo Zabaleta that saw him receive a yellow, while Yaya Toure stung Lloris' palms with a rasping drive and it took a brilliant tackle from Jan Vertonghen to stop Tevez from racing clear.
Andre Villas-Boas brought on Tom Huddlestone and Lewis Holtby in a double change and later Defoe for the ineffective Emmanuel Adebayor, with Tottenham reaping the benefits from the tactical reshuffle.
The equaliser came in the 75th minute when City backed off Bale and he whipped in a sublime low cross with the outside of his boot which Dempsey converted from close range.
The goal lifted Tottenham's spirits and they threw everything at City. The tactic paid off when Defoe latched on to Holtby's through-ball and curled a brilliant shot past Hart.
A carnival atmosphere broke out inside White Hart Lane and the roof nearly came off moments later when Bale killed the game off by lifting the ball over Hart after a brilliant pass from Huddlestone.