Substitute Eidur Gudjohnsen put Spurs ahead just 18 seconds into the second half when he nipped onto the end of a delightful chip from Peter Crouch to fire a left-foot shot into the roof of the net.
And things got worse for the home side four minutes later when Dean Whitehead was sent off for his second bookable offence after clattering Luka Modric in the centre circle.
But they drew level when Benoit Assou-Ekotto was adjudged to have fouled Dave Kitson in the box and Matthew Etherington sent Heurelho Gomes the wrong way from the penalty spot.
Assou-Ekotto redeemed himself, though, when he crossed for Niko Kranjcar to net the winner with 13 minutes remaining.
That saw Spurs capitalise on Aston Villa's draw against Wolves - a result which could have been even worse for Martin O'Neill's men.
John Carew salvaged a point for Villa after Wolves had looked set for their first win over their local rivals for 30 years, Jody Craddock's equaliser and James Milner's own goal putting them in front.
But Carew followed up his opener with his 13th goal of the campaign with only seven minutes remaining to make the final score 2-2, benefiting on each occasion from marginal offside decisions.
Hull slipped closer to relegation after a late capitulation at rock-beottom Portsmouth.
After Jan Vennegoor of Hesselink had headed against a post, Craig Fagan's strike was deflected into the net by Caleb Folan to give Hull the lead in the 27th minute.
But Pompey were level 10 minutes later as Jamie O'Hara's cross following a short corner bounced into the path of Tommy Smith, who back-heeled past Boaz Myhill.
Folan restored the Tigers' lead, beating the offside trap and producing a composed finish across keeper David James.
But O'Hara levelled two minutes from time with a superb curler after a 20-yard free-kick and Richard Garcia's howler saw Nadir Belhadj tee up Kanu to seal a dramatic 3-2 win.
Hugo Rodallega's injury-time header saw Wigan boost their own survival hopes with a deserved 1-0 win over Burnley.
The Latics created the most meaningful chance of the opening 45 minutes when Gary Caldwell struck the right-hand post with a firm header.
There was a delay early in the second period when Latics keeper Chris Kirkland appeared to be struck by an object thrown from the crowd, moments after Wigan were denied a clear penalty when Leon Cort brought down James McCarthy.
Wade Elliott cleared Rodallega's looping header off the line but the Colombian was not to be denied when he met Victor Moses' 93rd-minute cross.
Darren Bent's early brace set Sunderland on their way to a 3-1 win over Birmingham.
The striker stabbed home the first inside five minutes after Benjani Mwaruwari's shot was blocked and jinked inside Scott Dann to add a fine second six minutes later.
Cameron Jerome ran onto Michel's superbly weighted through-ball to halve the deficit with a neat curling finish but Fraizer Campbell grabbed a late clincher for the Black Cats.
Everton eased to a 2-0 win over Bolton at Goodison Park.
Wanderers were reduced to 10 men when last man Gretar Steinsson bundled over Yakubu as he raced clear and Mikel Arteta stepped up to double the punishment by curling a superb free-kick over the wall.
Leon Osman then laid the ball back for Steven Pienaar to slam in a late second.