Spurs had trailed for 70 minutes to Samir Nasri's opener but after Clint Dempsey poked home a leveller, quick-fire goals from Jermain Defoe and Gareth Bale followed to turn the game on its head.
Bale scored the third goal on his return from injury. The Wales international was subdued in a central role in the first half, but find more joy after moving on to the right-wing after the break.
"We spoke at half-time about it," Bale said. "They don't really play with wingers, they're quite compact in the middle, so the gaffer said at half-time there was more room outside and it proved a good move."
Although Bale killed City off with the third, it was his cross and Dempsey's finish that turned the game in the 75th minute.
"It just gave us that bit more belief that we could go on and win it," he said. "As soon as that went in it lifted us."
Spurs are now two points behind north London rivals Arsenal with a game in hand as the battle for Champions League football hots up, and Bale has no doubt about the importance of finishing in the top four.
"It's massive," he said. "The club's moving forward every year and all of us players want to be in the Champions League playing against the best week-in, week-out.
"We showed today [Sunday] that we're going to keep pushing to the end of the season to get in the top four."
Defoe who gave Tottenham the lead with a superb curling effort hailed his side's character after the match.
"Before the game we knew it was going to be difficult, they're a great team with great players, but towards the end there was great character, it was unbelievable," Defoe told Sky Sports 1.
"We played well and everyone dug in. The finish was unbelievable."
Defoe, who had been on the pitch only seven minutes when he scored, having returned from an injury lay-off, struck the second with a superb shot that beat Joe Hart from an angle.
"It was nice," he said. "As a forward, you always want to score goals. I've always said the most important thing is to get three points, but to get three points and get on the scoresheet, I'm delighted."