Goals from Roberto Firmino, Trent Alexander-Arnold and Sadio Mane capped a dominant display by Jurgen Klopp's side whose first league win since a 7-0 thrashing of Crystal Palace on Dec. 19 restored their place in the top four.
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Firmino's effort in first-half stoppage time ended Liverpool's barren run of 482 minutes without a league goal.
Alexander-Arnold doubled their lead in the 47th minute before Pierre-Emile Hojbjerg lashed in his first goal for Tottenham a minute later to give the hosts hope.
With Tottenham's defence unravelling, Mane struck again for Liverpool in the 65th minute and there was no coming back for Mourinho's side.
Both sides also had goals ruled out by VAR decisions.
Liverpool's seventh successive win over Spurs in all competitions moved them into fourth spot with 37 points from 20 games, four points behind leaders Manchester City who have played a game less. Tottenham, who could have gone above Liverpool with a win, stay sixth with 33 points.
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This was not quite Liverpool back to their best but it was an important statement of intent for Klopp's side that they will not be giving up their title without a fight.
Even with a makeshift central defensive partnership of Jordan Henderson and Joel Matip they were too strong for a Tottenham side who were culpable for all three goals.
"Nothing has really changed, we're the same team we always have been," Alexander-Arnold said.
"We have the same mentality going into games, we respect the opposition. We have the expectation on ourselves that we should win the game and it was a whole performance from the lads."
Liverpool should have ended their drought in the opening minutes when Mane was through on goal but steered his shot wide.
A few minutes later that miss looked costly as Son Heung-Min thought he had given Spurs the lead from Kane's pass but his effort was ruled marginally offside by VAR.
While Tottenham relied on counter-attacks, Liverpool looked the more threatening side and they were gifted the opening goal deep into stoppage time.
Mane was again the creator as he burst into the area and his shot was only pushed out by Lloris into the path of Alexander-Arnold to rifle in the rebound with his right foot.
Tottenham responded within a minute from an unlikely source as Hojbjerg sent a swerving effort past Allison from the edge of the area. In a frenetic passage of play Mohamed Salah then belted a shot past Lloris but Tottenham were spared by a VAR check which showed a harsh handball by Firmino in the build-up.
Ten minutes later another Spurs error, this time by central defender Joe Rodon, allowed a low cross to reach Mane who made no mistake.
On Kane's injury, Mourinho said: "Two ankles, the first was a bad tackle, it was [Liverpool's] Thiago [Alcantara], the second one I didn't know well.
"But two injuries in both ankles, the second one worst than the first one -- a few weeks, I don't know. There are some players you can't replace."
Klopp's side also endured yet more centre-back woes as Matip, who has battled to stay healthy all season, suffered a "serious" injury.
"If you have a center-half available who is a reasonable price, and who is of the quality we need, send me a message and I will go for it. It's not about [just signing a player]," Klopp said of possibly signing reinforcements ahead of the winter transfer deadline.