There were multiple chances to bolster the lead for Palace in the second-half, the pick of them fell to Casey who was once denied by the ‘keeper and then the offside flag as he was in search of his hat-trick.
Captain Jemide saw a header from a Cardines corner deflect off a Norwich defender before it was hacked away in the ensuing chaos.
Norwich did pull one back through Mundle-Smith 10 minutes from time. Eastwood made an initial stop to deny substitute Finlay Corke just moments before, though Mundle-Smith was played through after Corke pounced on a loose ball to slot in a consolation for the Canaries.
The host’s relatively muted celebrations were cut short as Agbinone restored the three-goal advantage with the pick of the bunch. After receiving it out wide from a George King pass, he cut inside and skipped past three Norwich defenders before hitting it back across goal and into the corner.
His fourth of the campaign sealed all three points for Palace as they saw the remainder of the game out. Victory puts an end to the five-game losing streak before this game and sees the side move to within three points of Arsenal in fifth place.
Norwich: Bullen (GK), Simbai (Owen, 60), T. Williams (Rowland, HT), Doy, Keita (Ofori-Manteaw, HT), Djedje, Sealey, Chilvers, Roberts (Corke, 68), Mundle-Smith, Daley (Mundle, HT).
Palace: Eastwood (GK), Cardines, Grante, Jemide, Trialist, Austin (King, 51), Gibbard (Mustapha, 53), S. Williams (Whyte, 88), Agbinone, Casey (Redhead, 88), Dashi.
Sub not used: Hill (GK).