Neil Warnock kept faith with the same 16-man squad that won 3-0 at Wolves last week and the Eagles boss was rewarded with another three-point haul in front of an increasingly-enthusiastic home crowd.
Clinton Morrison and Mark Hudson were on the scoresheet at the beginning an end of an entertaining Championship clash at Selhurst Park.
Palace roared out of the starting blocks and were ahead, albeit in slightly fortuitous circumstances, with just six minutes on the clock.
Jamie McAllister attempted to hook clear James Scowcroft's flick and the ball ricocheted off the left knee of the unwitting Morrison and beyond Adriano Basso in the visiting goal.
The Eagles were flying and should have doubled their advantage just two minutes later, but Ben Watson hesitated after being played in by another Scowcroft flick and the City defence regrouped and cleared the danger.
Soon after, Scowcroft went close with a long-range effort which whistled just the wrong side of the upright.
On-loan midfielder Shaun Derry, who was playing in his final game before returning to Leeds United, then saw his attempted lob held up in the wind before Tom Soares could only poke the ball wide of both Basso and the target.
City's only real chance of the first period had fallen to Liam Fontaine when his snap-shot ballooned high over the crossbar.
However, the Robins were almost back on level terms against the run of play right on the whistle, when debutant Nick Carle drew a fine save out of Julian Speroni and Clint Hill knocked the rebound narrowly wide of the mark.
The Robins looked much improved at the start of the second half and Carle again tested Speroni with a 48th minute header which the keeper did well to acrobatically turn away.
Michael McIndoe was next to try his luck when he ran through on goal, but the attention of John Halls forced the City midfielder to take his eye off the ball and he lashed a rising shot over the bar.
That seemed to rouse the home side from their slumbers and Morrison should have claimed his and Palace's second of the afternoon on the hour-mark.
However, after being put through by the impressive Watson, the in-form striker snatched at the chance and sliced his low shot wide.
But Palace were not to be denied and captain Hudson made sure of the points in the 85th minute, when he rose ahead of Basso to meet a cross and direct the ball into the empty net.