An evenly-matched first half got off to a lively start, with a sprawling Lewis Dunk clearing Mohamed Salah’s shot off the line within five minutes.
Up the other end, Trent Alexander-Arnold was in the right place at the right time to deny Evan Ferguson after good work from Solly March down the wing.
After being sent through one-on-one by Harvey Elliott, Salah surprisingly side-footed wide, but atoned for his miss when the roles were reversed for the opener minutes later.
Jason Steele got a hand to Elliott’s effort, yet couldn’t stop the ball from trickling into the far corner.
However, that lead lasted less than 10 minutes, as a partially-cleared corner fell to Tariq Lamptey, who tried his luck from range, seeing his effort deflect off Dunk to wrong-foot Alisson.
A couple of early second-half chances for the Seagulls prompted Jurgen Klopp into a triple change on the hour mark.
Having just come on, James Milner produced a perfectly-measured ball to set Salah in behind, but Steele remained composed to put a stop to the attack.
Armed with fresh impetus, the Reds pushed to retake the lead, but instead required Alisson’s quick reactions to remain level, as the Brazilian denied March from close range.
Brighton fans were left enraged when Alexis Mac Allister was knocked off the ball by Ibrahima Konate when through on goal, and Fabinho narrowly escaped a red card for a reckless challenge on Ferguson.
However, with time almost up, all was forgiven when a set-piece made its way to Mitoma, who displayed exquisite close control before firing in the winner.
Roberto De Zerbi’s side marked their cup progression with their first-ever consecutive pair of wins over Liverpool, while the Reds exit the FA Cup at this stage for a fifth time in seven years.
Flashscore Man of the Match: Kaoru Mitoma (Brighton & Hove Albion)