Liverpool are desperately trying to salvage their troubled campaign by qualifying for next season's Champions League via a top-four finish.
Beaten 3-1 by Real Madrid in the Champions League quarter-final first leg on Tuesday, Jurgen Klopp's side knocked West Ham out of fourth place in the most dramatic fashion at Anfield.
Liverpool had lost their previous six home league matches, but Alexander-Arnold clinched their first success in front of the Kop since December as the Reds avenged their humiliating 7-2 defeat at Villa in October.
Villa striker Ollie Watkins scored a hat-trick in that rout and he was back on the scoresheet after 43 minutes. Taking a touch from John McGinn's pass into the Liverpool area, Watkins hit a low shot that squirmed under Alisson Becker's weak attempted save.
Liverpool were denied an equaliser moments later when Roberto Firmino's close-range finish was chalked off by VAR for an extremely tight offside call against Diogo Jota in the build-up. But Mohamed Salah levelled in the 57th minute with a close-range header after Andrew Robertson's shot was parried into his path by Emiliano Martinez.
Villa winger Trezeguet hit the post in the second half, but Alexander-Arnold won it in added time when the right-back blasted home from the edge of the area.
In Saturday's late game, sixth-placed Chelsea will move above Liverpool into fourth place if they beat Crystal Palace at Selhurst Park.
Standout matches today