The Uruguayan netted twice to bring his goal tally for the season to 17 goals in just 11 Premier League games, as the Reds closed the gap on table-toppers Arsenal to two points.
Stand-in captain Luis Suarez scored twice as Liverpool piled extra pressure on Tottenham head coach Andre Villas-Boas with a dominant display.
Suarez, who now has 17 goals in 11 league outings this season, opened the scoring after excellent work from Jordan Henderson, and the midfielder doubled Liverpool's lead just before the break.
An out-of-sorts Tottenham struggled to pose any attacking threat and saw its hopes of fighting back take a blow when Paulinho was sent off in the 63rd minute for a high tackle on Suarez.
The visitors made the most of their advantage, adding further goals from Jon Flanagan, Suarez and Raheem Sterling.
Liverpool's 10th win of the season sees it leapfrog Everton, Chelsea and Manchester City in the table, while Tottenham remains seventh, eight points off top spot.
The hosts made two changes from their previous Premier League match, with Sandro and Roberto Soldado returning, while Lucas replaced Steven Gerrard (hamstring) in the only alteration to Liverpool's team.
Brendan Rodgers' side began the game well and took the lead in the 19th minute as Suarez punished some lax Tottenham defending.
Henderson dispossessed Michael Dawson inside the penalty area and the ball fell into the path of Suarez, who dodged gloriously past Kyle Walker and fired low under Hugo Lloris.
Tottenham were struggling to create anything and nearly fell two goals behind in the 28th minute as Philippe Coutinho hit the crossbar.
Nacer Chadli and substitute Lewis Holtby, who replaced the injured Sandro, wasted good chances for the hosts before Liverpool claimed a second goal before the break.
Lloris did well to deny Henderson and Suarez in quick succession, but the second save merely provided the England midfielder with a second opportunity, which he accepted with a well-placed volley from 10 yards.
Mamadou Sakho nearly gave Liverpool a great start to the second half as he met a Raheem Sterling cross at the back post, but his header hit the post and Martin Skrtel was unable to convert the rebound.
Despite gaining more possession Tottenham's task was made a lot harder just after the hour as Paulinho saw red for catching Suarez in the chest with a wayward right boot.
Flanagan thundered home his first league goal for the club, lashing into the top-right corner after Henderson's clever backheel had given Suarez the opportunity to cross.
There was still time for Suarez to find the net again with a nonchalant lob and the Uruguayan then set up Sterling for Liverpool's fifth in the 89th minute.