The Ghana international opened the scoring for The Eagles at Keepmoat Stadium in the eighth minute.
After receiving a pass from Luka Milivojevic in his own half, Schlupp went on a magnificent solo run into Rovers' penalty box before releasing a low shot into the bottom right corner of the net.
Max Meyer doubled the score for the Premier League side in first-half stoppage, the two goals ultimately proving enough to book a last-eight ticket in the cup competition.
Schlupp's strike was his fifth goal in all competitions for Palace this season, having failed to find the back of the net in his first two seasons with the club.
The tally also stands as his highest in a single campaign since hitting six goals for Leicester City in 2011-12.
Whereas Schlupp played the entirety of Sunday's fixture, compatriot and club-mate Jordan Ayew was hauled off on the hour mark, his place taken by Senegal's Cheikhou Kouyate.