Steven Gerrard scored twice to ensure there would be no repeat of the 1988 FA Cup final defeat for Liverpool at the hands of AFC Wimbledon.
The Anfield captain, who announced on Friday his exit from the club at the end of the season, headed Brendan Rodgers’ team in front in the 12th minute.
But Wimbledon hit back when a strong spell of pressure resulted in Adebayo Akinfenwa forcing the ball home after a Simon Mignolet error from a corner.
The interval came as a relief for the Premier League team who had been under the cosh, but Gerrard remained calm in the 62nd minute when he curled home a free-kick to see Liverpool through to the fourth round.