Curtis Jones was shown a straight red card early on in the game for going over the top of the ball and making contact with Yves Bissouma after just 26 minutes.
Son Heung-min put Tottenham in front ten minutes later but Reds hit back when Cody Gakpo levelled in first-half stoppage time.
Liverpool were then reduced to nine men as Diogo Jota was shown two quickfire yellow cards.
Yet the visitors held out until the 96th minute when Joel Matip turned Pedro Porro’s cross into his own net.
The three points take Tottenham above Liverpool into second, one point behind City, as they remain unbeaten in the Premier League under Ange Postecoglou.
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