The African duo spoilt the Whites' top-flight welcome party with goals in each half of Saturday's fixture.
Jean Michael Seri was handed his league debut after completing a permanent move from Nice last month while Zaha and Schlupp started the encounter for the visitors.
Schlupp opened the scoring in the 41st minute - his first EPL goal since 2015 [Leicester City v. Norwich].
Zaha then linked up with Aaron Wan-Bissaka to secure maximum points for the south London outfit in the 79th minute.
Seri was later replaced by Stefan Johansen in the 82nd minute while Neeskens Kebano watched the entire action on the bench. New signing Cheikhou Kouyate and Pape Souare were late substitutes for the Eagles.