Two goals in each half from John Oster, Sean Scannell, Craig Beattie and Jose Fonte secured Palace's well-deserved victory as Neil Warnock's men returned to winning ways after last Saturday's 2-1 defeat at Cardiff City.
Dele Adebola and Nicky Maynard hit City's consolations.
Palace made a blistering start to the game and found themselves 2-0 up within the opening 13 minutes.
First Oster coolly slotted past Adriano Basso after an inch-perfect pass from on-loan Beattie and then two minutes later and after some slack defending, Scannell fired Palace into a two-goal lead after Paul Ifill's lay off.
Ben Watson narrowly missed the target with a 20 yard free-kick in the 42nd minute before Adebola gave the Robins a major boost moments before the break by smashing home from six yards after a Marvin Elliott flick.
Palace started the second period in the same fashion as they started the first with Beattie going close with a dipping shot from the edge of the box three minutes after the restart.
And Palace hammered home their dominance in the 65th minute when Beattie fired past Basso after substitute Shefki Kuqi's low cross-cum-shot.
Portuguese defender Fonte rose above everyone to head home Watson's corner to extend Palace's lead in the 72nd minute.
Maynard pulled one back for City in the two minutes later after Fonte's poor goal-kick dropped to Adebola, who played in the substitute to coolly round Julian Speroni before slotting into an empty net.
But City's hopes of remarkable comeback failed to materialise with Palace missing a number of good chances to net a fifth as Warnock's men comfortably held on for all three points.