Palace started well at the Madejski, with Aaron Martin heading over from six yards out before Adam Le Fondre wasted a decent chance for the Royals.
Pogrebnyak missed the target and Danny Guthrie had a goalbound shot blocked right before half-time whistle blew.
Pogrebnyak (52) grabbed his first goal in the blue and white hoops when his shot was deflected past the Palace keeper to open the scoring.
The Royals were then two up when Hal Robson-Kanu's low cross found Le Fondre (54) and he made no mistake from close range.
Simon Church's header was well saved by Julian Speroni and Palace should have had an 89th minute consolation but substitute Jermaine Easter pulled his shot wide.