Alberto Paloschi put the visitors ahead at White Hart Lane after Angel Rangel’s effort fell to him in the 19th minute.
However, Mauricio Pochettino’s men equalised when Nacer Chadli deflected in Kyle Walker’s shot with 20 minutes left to play.
And Danny Rose then sent the home fans wild when he drove in the winner after Swansea failed to clear a corner.
The result moved Tottenham three points clear of local rivals Arsenal ahead of next weekend’s north London derby at White Hart Lane.
And Hoddle talked up the importance of the result on social media after the final whistle.
Such an important Win for Spurs today . Good mental Strength to come back . Now for the London Derbies !!
— Glenn Hoddle (@GlennHoddle) February 28, 2016
Tottenham now turn their attentions towards their trip to West Ham United on Wednesday night.
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