Boaz Myhill saved from Kenny Miller in the opening minute but could do nothing when Delaney deflected a cross from Ki-Hyeon Seol.
Myhill saved from Carl Cort while Hull's Nick Barmby had an equaliser ruled out for offside.
Hull manager Peter Taylor:
"For us to be in the Championship is a really big test and I've said all along Wolves would be one of the clubs up there challenging for promotion.
"In the first half Wolves produced lots of good moves, but we hung in there.
"In the second half we looked more confident in our chances of scoring a goal. Overall, I've been quite pleased with the way we played."
Wolverhampton: Oakes, McNamara, Lescott, Edwards, Naylor, Ricketts (Cameron 64), Ince, Seol, Kennedy, Miller (Clarke 87), Cort.
Subs Not Used: Olofinjana, Ikeme, Ndah.
Goals: Delaney 19 og.
Hull: Myhill, Wiseman, Delaney, Coles, Edge, McPhee (Elliott 38), Andrews (Green 33), Ashbee, Ellison, Fagan, Barmby (France 66).
Subs Not Used: Leite, Joseph.
Ref: L Mason (Lancashire).