Brendan Rodgers' men suffered a chastening 3-1 loss in south-east London earlier this season and the hosts suggested a repeat when Fraizer Campbell gave them a 15th-minute lead.
But Liverpool had only lost twice in 21 games across all competitions since that reverse last November and they brushed off a frustrating first half when Daniel Sturridge equalised with a fine volley after 49 minutes.
Adam Lallana scored decisively when a free-kick from substitute Mario Balotelli shortly before the hour proved too hot for Julian Speroni to handle, ensuring Palace could not muster a repeat of their famous semi-final triumph over the same opponents 25 years ago.
Dwight Gayle came off the bench to score twice in the dramatic 3-3 draw that dealt a decisive blow to Liverpool's Premier League title bid last season and the recalled forward was instrumental in the game's opening goal.
Martin Skrtel misjudged a punt forward from Joe Ledley, allowing Gayle to head at the on-rushing Simon Mignolet before Campbell slotted home the rebound.
A brilliant 20th-minute save by Speroni stopped Lallana - in for the cup-tied Jordon Ibe - from bringing Liverpool level when he smashed goalwards at the end of an intricate passing move, while home defender Scott Dann slid to block a drilled Philippe Coutinho effort.
Speroni was called upon again with half an hour played as Jordan Henderson arrowed in a swerving drive a minute before Palace debutant Pape Souare's clumsy challenge on Sturridge in the area went unpunished.
Lazar Markovic lashed over in the 41st minute but, despite their constant pressure, Liverpool required a sharp stop by Mignolet from Gayle to prevent them from being further behind at half-time.
Balotelli replaced fellow midweek goalscorer Markovic at the interval, while Palace boss Alan Pardew also sent on Jason Puncheon in place of Marouane Chamakh.
The patient build-up play Liverpool displayed throughout the first half was rewarded early in the second when Henderson floated a ball to the back post for Sturridge to volley firmly through Speroni's legs.
Palace bustled forward looking to restore their lead and Mignolet reacted well to turn Gayle's bobbing strike behind after a corner was partially cleared, but the turnaround was completed in the 58th minute with Balotelli to the fore.
Some quick footwork allowed the Italy international to draw a foul on the edge of the box from Scott Dann and Speroni could only block his resulting low free-kick into the path of Lallana, who made no mistake.
Set-pieces appeared to be Palace's best route back into the match as Mignolet punched uncertainly in the 63rd minute.
But it was a rare blot on an assured performance from the often-maligned Belgian goalkeeper, who was booked for time-wasting in stoppage time but played a full part in seeing Rodgers' team through to the last eight.
