Arsenal paid the price for missing a host of opportunities and were punished as Liverpool grew increasingly dangerous, the deadlock broken when Trent Alexander-Arnold's free-kick glanced in off Jakub Kiwior's head with seven minutes left.
Liverpool's triumph was completed in the closing seconds as a lethal break ended with Luis Diaz firing an emphatic finish high past Arsenal goalkeeper Aaron Ramsdale.
Mikel Arteta's side dominated the first half, with Martin Odegaard hitting the bar while Reiss Nelson and Kai Havertz also had chances to give Arsenal reward for their pressure.
Liverpool, despite missing captain Virgil van Dijk through illness and with Mohamed Salah at the Africa Cup of Nations, held firm and were always a threat. Alexander-Arnold hit the bar in the first half and as they grew into the game, Ramsdale saved well from Diaz and Diogo Jota headed against the woodwork.
Just as the replay that neither Arsenal nor Liverpool would have particularly wanted loomed, the unfortunate Kiowor headed past Ramsdale then Diaz ensured Jurgen Klopp's side would progress to the fourth round.
-- Courtesy of BBC Sport