Palace overcame a determined Walsall to book their place in the second round.
The lively Mark Wright hit the bar and Jorge Leitao's volley was tipped on to the post by Julian Speroni as the Saddlers started the game brightly.
Palace's Wayne Andrews missed an open goal before Tony Popovic scored from the spot after Danny Butterfield's shot had struck Daniel Fox on the arm.
Danny Granville curled a 25-yarder home and Hughes then tapped in after Oakes parried substitute Lewis Graban's shot.
Crystal Palace: Speroni, Fray (Togwell 64), Popovic, Hudson, Granville, Black (Grabban 85), Hughes, Riihilahti, Butterfield, Andrews, Kolkka (Berry 78).
Subs Not Used: Kiraly, Ryan Hall.
Booked: Hudson, Andrews.
Goals: Popovic 51 pen, Granville 83, Hughes 87.
Walsall: Oakes, Pead, Westwood, Bennett, Fox, Standing, Osborn, Smith (Larrosa 75), Wright, Merson, Leitao.
Subs Not Used: Gerrard, Kris Taylor, Kinsella, Coleman.
Booked: Larrosa, Westwood.
Ref: J Singh (Middlesex).