Georginio Wijnaldum scored away from home in England's top flight for the first time and Roberto Firmino gave Jurgen Klopp's men breathing space in the 54th minute.
Mauricio Pochettino's Spurs were again out of sorts following their 2-1 loss to Watford before the international break, with substitute Erik Lamela's stoppage-time goal giving the scoreline a very flattering look for the hosts.
Liverpool thought they had the lead inside 45 seconds when Firmino touched James Milner's excellent cross beyond Michel Vorm, but Sadio Mane prodded at the Brazilian's effort from an offside position.
Vorm stood firm when a slack pass from Eric Dier allowed Mohamed Salah a run at goal but Tottenham's goalkeeper – playing once more in place of injured captain Hugo Lloris – was culpable when Liverpool took the lead six minutes before half-time.
Following a botched punch from a corner, Vorm could only paw Wijnaldum's header away from behind his goal line.
More sloppy play from Tottenham after the break gave Vorm the opportunity to atone for his error with a sharp stop from Mane, before Lucas Moura found space at the other end to shoot against the outside of Alisson's right post.
A post was also involved in Liverpool's second as Jan Vertonghen slid in to block Mane's low cross, Vorm was unable to gather the rebound and Firmino converted from point-blank range.
It should have been 3-0 after the hour as Mane delayed his pass to Naby Keita and Vorm pushed the resulting shot over.
Firmino limped off before Vorm's mixed outing concluded with a stop from Salah.
Such wasteful finishing set up late drama as Lamela pounced on slack set-piece defending before Mane escaped a penalty shout for an untidy challenge on Son Heung-min.
61 - Roberto Firmino has been directly involved in 61 Premier League goals for Liverpool under Jurgen Klopp (38 goals, 23 assists), 16 more than any other player. Star. #TOTLIV pic.twitter.com/JpP8LY6UwW— OptaJoe (@OptaJoe) September 15, 2018
What it means: Liverpool's title credentials stand up to first major test
Four wins from four in the opening stretch of the season spoke well of Liverpool's ambitions without them ever quite hitting top gear, but the relative ease with which they dispatched Spurs counts as a statement. Back-to-back defeats and impressive starts from their rivals mean Tottenham already look more like top-four aspirants than title challengers.
Pat on the back: Tireless Milner drives Reds triumph
Liverpool's impressive close-season in the transfer market threatened to consign Milner to a bit-part role but the former England midfielder appears more vital to their cause than ever. Tottenham's extra man in midfielder rarely told as Milner commanded central areas in a typically tireless performance, as Jordan Henderson and the still unused Fabinho looked on from the bench.
Boot up the backside: Pochettino's diamond fails to sparkle
The logic of trying to outnumber Liverpool in central areas and give Spurs' defenders extra passing options against the visitors' press was sound. However, Pochettino's midfield diamond only sowed confusion and nullified Tottenham's usual threats. Failing to build on that statement 3-0 win at Manchester United last month feels awfully wasteful.
Key Opta stats:
- Tottenham v Liverpool is now the highest scoring fixture in Premier League history (152 goals).
- Tottenham have lost consecutive Premier League games for the first time since the final two games of the 2015-16 season.
- Georginio Wijnaldum’s goal for Liverpool came via his 55th shot attempted in away Premier League games.
- Tottenham faced 10 shots on target in a Premier League home game for the first time since January 2014 vs Manchester City.
- Christian Eriksen's assist for Erik Lamela's goal was his 50th in the Premier League, making him the second player to reach that milestone for Spurs (Darren Anderton, 67).
A mouth-watering Champions League clash at home to Paris Saint-Germain awaits Liverpool before they welcome Southampton to Anfield next weekend, while Spurs' forthcoming double-header consists of trips to Inter and Brighton and Hove Albion.