The Reds broke the deadlock at the conclusion of a hugely eventful first half when Sadio Mane scampered into space and squared for Roberto Firmino to slot in from close range.
Alexander-Arnold doubled the champions’ advantage immediately after the break, rasping home after Hugo Lloris had saved an initial shot from Mane.
Spurs reduced the arrears within two minutes via Pierre-Emile Hojbjerg’s swerving drive from the edge of the box, but Mane thumped in a third on 65 minutes to ensure maximum points were secured.
The result moves Liverpool into fourth place in the standings, four points behind leaders Manchester City.