Roberto Firmino's 90th-minute header downed Jose Mourinho's Tottenham in an engrossing top-of-the-table clash at Anfield.
Mohamed Salah had opened the scoring via a huge deflection before Heung-min Son's smash-and-grab leveller.
They slip three points behind the reigning champions, who have landed the first significant blow in the title race.
Story of the match
The pattern of the first half proved entirely predictable.
Liverpool, operating with trademark intensity, hemmed a regimented Spurs into their own defensive third. Firmino and Salah both Hugo Lloris in the early part of the contest.
And shortly before the half-hour mark, the breakthrough arrived.
The outstanding Curtis Jones weaved his way into the box and the ball ricocheted to Salah, who aimed for the bottom left corner, only to see his shot strike Toby Alderweireld. It seemed to hang in the air before landing in the opposite side of Lloris' goal.
Jones threatened a second within two minutes when he robbed a dallying Serge Aurier and cut inside, but Lloris was equal to the low shot.
What made the half especially predictable, though, was the abrupt manner of Spurs' equaliser.
In a rare moment of respite from the Red onslaught, Giovani Lo Celso picked up the ball and drove forward. When he reached the halfway line, he saw that Son was ready to set-off and promptly threaded a pass into the space behind the high Liverpool line.
The indomitable South Korean opened his body as if to create an angle for a cross-goal finish, but then intelligently tucked the ball beyond Alisson at his near post.
A swift VAR check showed he had timed his run to perfection.
This was Mourinho's blueprint in action. 21% possession, one-shot against Liverpool's eight, but a goal apiece.
The second half, by contrast, was evenly-matched. Indeed, the third quarter of the game actually belonged to Spurs.
Within two minutes of the game's resumption, Rhys Williams' wayward header had unleashed Bergwijn, who held off the challenge of Trent Alexander-Arnold but erred in opting for an outside-of-the-boot finish which spun harmlessly away from goal.
Somehow an even better chance was to arrive just over 15 minutes later. The position was similar but the circumstances more favourable. After latching onto Son's flicked header, the Dutchman could bear down goal without facing resistance.
The goal, as they say, was at his mercy, but he stroked his shot onto the inside of the far post and Fabinho rushed back to thump the ball to safety.
The resulting corner should have banished Bergwijn's guilt. The largely peripheral Kane wriggled free of his man and had a free header six yards from goal, but skewed it down into the ground and over the crossbar.
Curiously, it might have taken those monumental let-offs to convince Liverpool that it may just be their night.
They started to threaten again. Salah should have done better when Williams set him away, and Sadio Mane blasted the crossbar after shrugging off Aurier, Spurs' most dogged defender.
Mourinho, recognising his side had had their moments, sent on Sergio Reguilon and moved to a back five in a bid to ensure the point.
Liverpool's set-piece routines had brought very little joy and Spurs' organisation had again been superb. No reason to fret, then, when the clocked reached 90 and Mane won a corner?
This time, Andrew Robertson kept his delivery simple. He swung it cleanly to the back post, where Firmino waited. The Brazilian has fumbled a catalogue of gilt-edged chances in recent times but this was a measured, magnificent header. He powered it back across and goal, leaving Lloris a spectator.
His euphoric charge to the 2,000 supporters on the Kop - the only supporters, incidentally, attending a midweek Premier League match - represents the first truly iconic moment of Liverpool's title defence.
Man of the match - Curtis Jones
Jordan Henderson and Fabinho were excellent for Liverpool. The match-winner Roberto Firmino is well and truly back. But the best player on the pitch was Curtis Jones, who last season still seemed some years from a meaningful first-team breakthrough.
The 19-year-old's development has accelerated to a breathtaking extent. He is manipulating Premier League matches. On this, the most important outing of his career so far, he looked the most likely to plot a way through Mourinho's infamous low block.
His ambition led to the first goal and he very nearly fashioned a second for Sadio Mane.
Naby Keita did not come on until stoppage time and Alex Oxlade-Chamberlain was an unused substitute. Jones' involvement should not be seen as enforced. It is his spot, and he does not look like a young man who will accept being dislodged.