Luis Garcia's strike earned Liverpool a third away win this season to take them up to fourth as Spurs were left to rue a host of missed chances late on.
The winner owed much to an error from Didier Zokora, which led to Spanish striker Garcia sweeping in after Steven Gerrard had been gifted possession.
Dirk Kuyt also came close, but a late Spurs assault so nearly bore fruit.
Steve Finnan hit his own bar and Hossam Ghaly twice contrived to fire wide with the goal gaping, but the Reds held on.
It represented Spurs' first home defeat in 13 games, but Martin Jol will wonder how his side did not emerge with at least a point after a thrilling conclusion to the game.
However, the hosts, disjointed in the absence of skipper Ledley King, did themselves few favours as they took an age to get into the match.
Despite Mido blazing wide from 18 yards when well-placed on 10 minutes and an effervescent performance from Jermain Defoe, it was Liverpool that edged the first hour.
Robinson had to save low twice from Craig Bellamy efforts and Kuyt curled wide when well-placed, but the half looked to be drifting towards stalemate until Garcia's intervention.
After a Liverpool attack had broken down, Zokora spilled a pass to Gerrard and, after exchanging passes with Kuyt, the midfielder's effort bobbled to Garcia who swept home left-footed.
The second half started much like the first, with the visitors looking dangerous on the break as the hosts struggled to find their rhythm.
Spurs stood firm though, despite Kuyt and Steven Gerrard going close, and, with 20 minutes remaining, they launched their assault.
With the rain lashing down, silky football made way for harem-scarem stuff, and Tottenham camped themselves in the opposition half.
Dimitar Berbatov's arrival lifted crowd and team alike and the Bulgarian almost helped bring the hosts level on 75 minutes, his clever run and pass ending with Steve Finnan rocking his own bar with a defensive header.
Minutes later, Spurs broke clear again, this time Ghaly contriving to blast wide from three yards with Reds keeper Pepe Reina stranded on the deck.
It was an enthralling conclusion, with the visitors still looking good on the break, but Tottenham were left to rue their profligacy once again when Ghaly failed to poke home awkwardly when Defoe's strike was only parried by Reina.
There was still time for the hosts to see Gerrard's own 'goal' correctly ruled out for offside and Berbatov to finish tamely from 12 yards when clear but Liverpool held on to reignite their Champions League push.
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