Samir Nasri put City in front before the break and it looked as though Roberto Mancini's men were going to return to Manchester with all three points.
However, Spurs rallied in the second half and a goal from Bale accompanied by strikes from Clint Dempsey and Jermain Defoe kept the club's chances of qualifying for next season's Champions League alive.
"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," the winger told Sky Sports News.
Next up for Tottenham is a trip to Wigan Athletic.