Harvey Elliott put Liverpool ahead with a low shot into the far corner following a clever pass from Mohamed Salah in the 30th minute.
Lewis Dunk equalised for Brighton nine minutes later with a flick on a long-range effort from Tariq Lamptey, which deflected into the goal and left goalkeeper Alisson Becker wrong-footed.
The score remained 1-1 until Mitoma found the net in the 92nd minute with a fine finish. Mitoma controlled the ball on the half-volley before firing home a dramatic late winner.
The result was the second time Brighton defeated Liverpool this month, having already beaten Jurgen Klopp's side 3-0 in a Premier League game.
Salah missed a good chance in the second half and so did Solly March for Brighton. Despite their efforts, neither side was able to break the deadlock until Mitoma's decisive goal.
Liverpool's exit from the FA Cup marks a disappointment for the defending champions and serves as a reminder of the competitiveness of the tournament. The result also highlights the strength of Brighton, who will be looking to build on this win and continue their impressive run.