Mark Hudson and Shefki Kuqi fired Palace into a two-goal lead by the half-hour and, although Robert Earnshaw pulled one back for the Canaries, Stuart Green restored Palace's two-goal lead on the stroke of half-time.
Yet for the first 20 minutes Norwich were completely on top. Darren Huckerby was in rampant mood during this period and hit the underside of the bar as well as forcing Scott Flinders to pull off a tremendous diving save.
Against the run of play, Palace went in front on 26 minutes. Green's deep corner was headed back across goal by Leon Cort and Hudson at the opposite post nodded down past the stranded Paul Gallacher.
On 29 minutes Palace doubled their lead after Dougie Freedman picked up a loose ball just inside his own half. The striker made headway towards the penalty area before slipping a perfect pass into the path of Kuqi who, from 15 yards out, fired past the advancing Gallacher.
The Eagles were at long last in confident mood and Marco Reich should have added a third but his shot screamed past the upright. The German winger landed awkwardly as a result and was eventually replaced at half-time. By then Earnshaw had converted from the penalty spot with a rising right-foot shot after Carl Fletcher had handled.
But any hope of a comeback was short-lived as, almost immediately, Kuqi pulled the ball back from the byline and Green drove fiercely into the top corner to give Palace a somewhat flattering 3-1 lead at half-time.
After the break Norwich continued to plug away, but it was Palace that came closest to scoring. Cort headed just over, Hughes was about to score until Gary Doherty stormed in with a crucial tackle and Freedman drilled wide as Palace enjoyed a decent spell.
At the other end, substitute Dion Dublin missed a great chance and Earnshaw really should have done better but lofted his shot over the bar.