Jurgen Klopp's side, who were beaten 3-0 at the Seagulls two weeks ago, took the lead midway through the first half when Harvey Elliott slotted into the bottom corner from Mohamed Salah's pass following a quick break.
However, Brighton equalised when Tariq Lamptey's shot from distance deflected heavily off Lewis Dunk to fly into the back of the net.
It looked like a replay at Anfield would be needed to decide the tie before Mitoma stepped up to snatch another big result for Brighton.
Seagulls continue to defy expectations.
Seagulls boss Roberto de Zerbi since his appointment that you couldn't say with a degree of certainty which side was the favourite heading into this match.
Liverpool won the FA Cup last season but have endured a difficult campaign and went into this game as the side lower in the Premier League table - they are ninth while Brighton are sixth.
The hosts impressively outplayed the Reds on 14 January and clearly fancied their chances of another victory against them as they showed belief and confidence in this game.
Great defending by Dunk prevented what looked to be a certain goal for Salah early on, while Evan Ferguson then had a shot cleared off the line by Trent Alexander-Arnold.