Mo Salah’s first-half double put Jurgen Klopp’s side on course for all three points in the capital but Harry Kane reduced the deficit with 20 minutes left.
Antonio Conte’s Spurs pushed for a late leveller but were thwarted by a dogged Liverpool, who closed the gap between the sides to seven points and with a game in hand on the fourth-placed hosts.
After struggling for consistency for much of the season, Klopp would have been encouraged by a professional display to win their first away league game of the season and back up Tuesday’s triumph over Napoli.
Both teams entered this fixture following important midweek victories in the Champions League, but Spurs’ came at a cost with Son Heung-min suffering a fracture around his left eye.
Liverpool boss Klopp rewarded Darwin Nunez for his goal against Napoli with a start and the Uruguayan twice went close in the opening exchanges with one volley parried away by Hugo Lloris before another curler went wide.
The visitors had settled quickly and it was no surprise when they went ahead with Nunez and Salah combining in the 11th minute.
Andrew Robertson, rested on Tuesday, crossed into the area for Nunez, who controlled well and spun away from his marker before he teed up Salah, who took a touch and fired into the bottom corner in a flash.
Tottenham’s tendency to start slowly had again cost them but the hosts did respond well to going behind and hit the woodwork after 15 minutes.
Kane produced a dangerous cross into the area that Perisic missed and Alisson Becker could only inadvertently divert the ball onto his own post after making a mess of his attempted punch.
Referee Andrew Madley waved away penalty appeals soon after when Ryan Sessegnon went down after a shove from Trent Alexander-Arnold in an incident that looked similar to the one that saw Manchester City defender Joao Cancelo sent off on Saturday.
Alexander-Arnold was on the back foot again midway through the first half when Eric Dier produced a superb crossfield pass to Sessegnon, who got in behind the Liverpool full-back but Ibrahima Konate came across well to get his team-mate out of trouble.
Conte’s side were looking the more likely but five minutes before half time they were undone by a poor Dier mistake.
Dier attempted to head Alisson’s clearance back to Lloris but got it horribly wrong and the ball bounced off his shoulder into the path of Salah, who raced through before he lobbed in for his second goal.
Liverpool were halfway to a vital victory for their top-four hopes but Spurs had come from two down to win at Bournemouth last weekend and should have reduced the deficit early into the second half.
First Dier headed straight at Alisson from Perisic’s corner before Spurs hit the woodwork for a second time when Sessegnon cut back for Perisic, but he flicked against the crossbar from close range.
Sessegnon flashed another effort wide moments later but Salah squandered a good chance to put the game to bed when he fired straight at Lloris in the 53rd minute.
The opportunities kept on coming for Tottenham, who saw Kane head Ben Davies’ free kick wide before Conte called for the cavalry with Matt Doherty and Dejan Kulusevski introduced with 22 minutes left.
Kulusevski’s entrance was met with huge cheers after he missed 11 matches with a hamstring issue and he quickly made up for lost time.
Barely 60 seconds had passed when Kulusevski passed into Kane, who rifled home first-time for his 12th goal of the campaign.
Clement Lenglet and Rodrigo Bentancur failed to score with headers from good positions with the seconds ticking away in London.
Lucas Moura was thrown on by Conte but, after Bentancur could not get on the end of Kane’s flick, Liverpool held on to make it back-to-back wins to move up to eighth.