Liverpool kept themselves on the fringes of the title race with a consummate away performance at Selhurst Park.
Goals from Steve McManaman, Michael Owen and Oyvind Leonhardsen restored some battered pride after last week's depressing home defeat at the hands of Manchester United.
It left Steve Coppell's Palace side still the only side in the country not to register an official home league win.
To add to the Eagles' woes, both of their Italian stars Michele Padovano and Attilio Lombardo limped off before an hour had gone.
Padovano lasted just 34 minutes and, after he had created Palace's two best chances, his substitution precipitated a home collapse.
Four minutes after he hobbled into the dressing room Liverpool were in front, McAteer's corner deflected off Lombardo and McManaman found an embarrassing amount of room in the area to blast a volley past Kevin Miller.
The second goal followed a depressingly familiar pattern, Lombardo had been struggling since the fifth minute and eventually admitted defeat 49 minutes into his comeback from a hamstring injury.
Six minutes later Liverpool doubled their lead with a sublime goal in the best Anfield tradition.
Redknapp's quick feet and quicker brain dissected the Palace defence with a superb ball inside Andy Linighan.
Owen beat Linighan easily for pace and as Miller advanced calmly chipped the ball nonchalantly over the stranded keeper.
That killed the game as a contest and as Palace piled forward desperately they were caught again on the break.
Owen had plenty of space to measure his cross and as Fowler and McManaman politely declined the opportunity, Leonhardsen fired home from 10 yards.
Palace had welcomed back skipper Andy Roberts after a two-week absence and Coppell also recalled Lombardo after an even longer absence, the former Juventus player having recovered from a hamstring injury.
Liverpool made one change from the side beaten 3-1 by Manchester United last Saturday, Steve Harkness replacing Stig Bjornebye who dropped down to the bench for the first time this season.
They had hoped to bring back Paul Ince after his suspension but the England midfielder has picked up a groin injury and he had to settle for a place on the bench.
The visitors started as brightly as their garish away strip, with Fowler and Owen looking particularly dangerous up front.
Fowler sold Linighan an outrageous dummy only for Paul Warhurst to sweep up well.
Owen then got to the by-line and pulled back a dangerous low cross but with McManaman just about to bury the simple chance Dean Gordon made a superbly timed challenge to scramble it away for a corner.
Despite their bright opening it was Palace who went closest to taking the lead, Shipperley's cross met perfectly first time by Padovano and David James had to pull off a superb one-handed save.
The £1.7million signing from Juventus forced another good save from James with a low left-foot drive which the keeper was happy just to palm wide for a corner as Shipperley closed in.
That was Padovano's last significant contribution however as he limped off and after Lombardo had gone Palace were fighting an uphill battle.
Their best chance came from a terrible mistake by James, who had been highly impressive up until the 70th minute.
He flapped wildly at a right-wing corner and succeeded only in palming the ball behind him and was grateful to see McManaman on the line to scoop the ball clear.
Liverpool continued to be dangerous on the break and Fowler could have had two himself in the second half.
First, he produced a fine full-length save from Miller with a delicate effort destined for the far corner.
And he forced Miller into another reflex stop a few minutes later with a stinging right foot shot following another lightning-quick break.
Palace had one ferocious appeal for a penalty turned down near the finish but in truth it would have made little difference.
Crystal Palace: Miller, Edworthy, Gordon, Roberts, Linighan, Lombardo (Ginty 49), Warhurst, Shipperley, Padovano (Emblen 34), Hreidarsson, Fullarton.
Subs Not Used: Nash, Zohar, Quinn.
Booked: Fullarton, Emblen.
Liverpool: James, Kvarme, McAteer, McManaman, Leonhardsen (Bjornebye 89), Fowler, Redknapp, Harkness (Berger 89), Owen, Matteo, Carragher.
Subs Not Used: Ince, Nielson, Rizzo.
Goals: McManaman 39, Owen 56, Leonhardsen 61.
Ref: N S Barry (Scunthorpe).
League position: 6th (28 points after 17 matches).
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