Carl Cort appeared to have won it with a drilled finish seconds earlier but Reich headed in from close range.
Inigo Idiakez's 25-yard free-kick put Derby 1-0 up before Kenny Miller nodded Wolves level from a Rob Edwards cross.
Joleon Lescott edged the visitors ahead with a powerful header but the Rams drew level through an Idiakez spot-kick which had be to taken three times.
Wolves manager Glenn Hoddle:
"I think I must have run over six black cats since I've been at
"I didn't think it was a penalty in the first place - that's my opinion but
that doesn't matter much, then the farcical stuff started.
"I believe the first retake was for encroachment and then Michael Oakes made
a magnificent save but the ref gave another retake - and it was inevitable that
they would score.
"In my opinion it was poor decisions and they've gone against us."
Derby: Camp, Kenna, Mills, Huddlestone, Makin, Smith (Reich 86), Bolder, Idiakez, Junior (Peschisolido 45), Rasiak, Tudgay (Taylor 45).
Subs Not Used: Grant, Konjic.
Goals: Idiakez 9, 77 pen, Reich 90.
Wolverhampton: Oakes, Edwards, Lescott, Craddock, Naylor, Seol, Olofinjana, Ince, Kennedy, Miller, Cort.
Subs Not Used: Jones, Andrews, Cooper, Clarke, Bjorklund.
Booked: Lescott, Oakes.
Goals: Miller 12, Lescott 72, Cort 90.
Ref: I Williamson (Berkshire).