The 19th minute penalty came after Kenny Miller was brought down by Rams goalkeeper Lee Camp, who was sent off, with Lee Grant coming on his place.
Wolves took just five minutes of the second half to double their lead when Miller was fouled by Adam Bolder and Cooper curled the ball home.
Derby boss George Burley:
"I didn't think the referee had any option but to send Lee Grant off.
"Wolves didn't create another chance at 1-0 but I didn't think there was any
way back once we went 2-0 down."
Wolverhampton: Oakes, Lowe, Craddock, Bischoff, Kennedy,
Cooper, Cameron, Olofinjana, Seol (Newton 69), Miller, Cort (Clarke 79).
Subs Not Used: Murray, Naylor, Andrews.
Goals: Cooper 19 pen, 50.
Derby: Camp, Jackson, Mills, Johnson (Huddlestone 45), Vincent,
Smith (Holmes 67), Taylor, Bolder, Reich (Grant 18), Rasiak,
Subs Not Used: Junior, Peschisolido.
Sent Off: Camp (16).
Ref: D Gallagher (Oxfordshire).