Roberto Firmino's last-minute header broke Tottenham's stubborn resistance at Anfield and sent Liverpool to the top of the Premier League table.
An entertaining encounter looked set to end in stalemate before - with the game entering stoppage time - Firmino soared to flash a header high past Spurs keeper Hugo Lloris from Andrew Robertson's corner.
Liverpool flew at Spurs in the opening exchanges and went ahead when Mohamed Salah's shot took a big deflection off Eric Dier and looped over Lloris.
Spurs had barely left their own half but struck with a counter punch seven minutes later when Son Heung-min raced clear to slip a composed finish past Alisson.
Spurs had the better chances in the second half, with Steven Bergwijn firing wide then hitting a post when clean through and Harry Kane heading over from point-blank range.
Manager Jose Mourinho was left to regret those missed opportunities as a late Liverpool surge ended with Firmino's winner to send the defending champions three points clear at the top of the table and inflict Spurs' first Premier League loss since the opening weekend home defeat against Everton.
