The 19-year-old striker bagged his 15th league goal of the season in the 22nd minute after Darren Purse headed Jason Koumas' left-wing cross into his path.
Leon Cort responded immediately but his goal was ruled offside, while Jon Parkin hit the post and Cardiff keeper Neil Alexander made some fine saves.
Hull manager Peter Taylor:
"I think we deserved at least a point, particularly with the second-half chances we made.
"We were second best in the first half but I still cannot believe our performance after the interval didn't bring us at least one goal.
"I think we should have had a penalty instead of a free-kick on the edge of the box, I'll watch the video with interest."
Cardiff: Alexander, Barker, Purse, Cox, Scimeca, Whitley, Ardley, Koumas, Ledley, Thompson, Jerome (Weston 83).
Subs Not Used: Margetson, Boland, Mulryne, Ndumbu-Nsungu.
Goals: Jerome 22.
Hull: Myhill, Thelwell, Cort, Delaney, Rogers, Paynter (Duffy 59), Andrews, Noble, Ellison (Elliott 63), Parkin, Fagan (Green 63).
Subs Not Used: Duke, Stockdale.
Ref: B Curson (Leicestershire).