Hugo Lloris was called into action almost immediately, pulling off a stunning reaction save from former team-mate Gylfi Sigurdsson in the opening minutes, before Erik Lamela shot over at the other end.
The first half was an end-to-end affair and Harry Kane should have give Spurs the lead when latching on to a Kyle Walker cross, only to see Swansea take the lead through Alberto Paloschi’s first Premier League goal.
Swansea started sitting back as the hosts’ dominance grew, but were again guilty of poor finishing with Heung-min Son firing straight at Lukas Fabianski when through on goal before Eric Dier did similar.
Fabianski was again on hand to deny Spurs after the break, pushing away a Christian Eriksen free kick that looked destined for the top corner before another effort by the Dane flashed past the post.
Mauricio Pochettino replaced Erik Lamela with Nacer Chadli and finally the breakthrough was made as the substitute beat Fabianski from the edge of the area before Danny Rose did similar minutes later.
The three points sees Tottenham keep pace with Permier League leaders Leicester City and open up a three-point gap over third-placed Arsenal, who lost 3-2 at Manchester United.
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