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.