Cort headed home six minutes from time as Wolves extended their unbeaten run to 20 games and ensured Palace have still not picked up a point this term.
The hosts took the lead when Ki-Hyeon Seol converted Cort's cross and Kenny Miller nearly doubled the advantage.
Palace were level when Jobi McAnuff slammed in a fine shot from the edge of the box only for Cort to deny them.
Crystal Palace manager Iain Dowie:
"It was a very good display. We were positive and more than matched them in football terms.
"It was much improved from Saturday and had to be. The players deserved more than that because it was a performance full of desire and good football.
"We have to maintain that standard. If teams are raising their game against us, we have to deal with that."
Wolverhampton: Oakes, Naylor, Lescott, Craddock (Edwards 63), McNamara, Seol (Clarke 64), Olofinjana, Kennedy, Ricketts, Miller (Ndah 78), Cort.
Subs Not Used: Ikeme, Cameron.
Goals: Seol 4, Cort 84.
Crystal Palace: Kiraly, Borrowdale (Hudson 89), Fitz Hall, Ward, Boyce, McAnuff, Watson, Leigertwood (Andrews 87), Soares (Kolkka 86), Macken, Johnson.
Subs Not Used: Butterfield, Speroni.
Booked: Soares, Fitz Hall.
Goals: McAnuff 42.
Ref: R Styles (Hampshire).