As if to emphasise the nostalgia, Liverpool were even parading the league title at half-time, the triumphant ladies team earning applause for a championship secured last week.
To say Palace were generous opponents is an understatement. Rarely has a side looked so ill-equipped for this standard of football, especially without possession.
Ian Holloway's side improved in the second half, but the game was over by half-time, Liverpool scoring three when seven would not have been flattering, the combination play between Suarez and Daniel Sturridge carving through what passed for a defence in name only.
Suarez had emerged from the tunnel prior to kick-off carrying his new born boy Benjamin and what followed amounted to his wetting the baby's head as he guzzled all on offer.
The Uruguayan struck the first on 14 minutes, exchanging passes with the overlapping Jose Enrique and somehow maintaining balance to poke beyond Julian Speroni.
Three minutes later, Enrique's 30 yard ball fell to Sturridge who engaged Simon Delaney in a game of twister prior to slamming across Speroni into the far post.
It seemed too easy, the fixture already carrying the hallmarks of a stroll.
Palace briefly rallied, showing more enterprise with the ball than without it. Jimmy Kébé delayed when sent clear with just Simon Mignolet to beat, his sliced effort cleared on the line by Kolo Toure.
Mamadou Sakho was also relieved when a sliced clearance fell the right side of his own post, just an inch wide.
Liverpool still looked like they'd increase their advantage with a gentle push on the pedal, although there was some dispute about the third from the penalty spot on 37 minutes.
Raheem Sterling, utilised as a right wing was adjudged to have been tripped by Dean Moxey inside the post, replay suggesting any significant contact was outside.
Steven Gerrard struck his 99th league goal for the club from the resulting spot-kick.
Liverpool showed some mercy at the start of the second half, significantly reducing the tempo as Speroni was given some respite, demonstrating a recurring flaw of failing to sustain a 90 minute performance.
Palace were encouraged on 76 minutes when substitute Dwight Gayle flicked in Jose Campana's free kick. It punished Liverpool lethargy after the break, but never threatened an outcome which had been determined much earlier.