Brighton & Hove Albion 2 Hull City 1
Brighton boss Mark McGhee caused a surprise before the game by dropping top scorer Leon Knight for the third time in seven matches.
Stuart Elliott gave Hull City manager Peter Taylor a dream start on his return to the club he guided to promotion in 2001-2002, when he gave the visitors a fifth-minute lead.
The Northern Ireland international flicked in a volley from close range after a corner by Andy Dawson had been headed goalwards by Leon Cort.
Carole hauled Brighton level 11 minutes later. The former Monaco winger cut inside to strike a left-foot shot over Tigers keeper Boaz Myhill and into the top corner from 20 yards.
Alan Blayney, making the last appearance of his loan spell from Southampton, made two important saves to keep Brighton on terms.
He dived to his right to keep out Nick Barmby's header and produced a similar stop from a free-kick by Dawson.
The value of those saves was emphasised when Oatway put the hosts ahead on the stroke of half-time. Fed by Paul Reid, the midfielder rifled a shot from 20 yards beyond Myhill for his first goal since March.
The second half was much scrappier than the first, but Hull twice came close to an equaliser.
Damien Delaney had a looping header from a corner nodded off the line by Reid and Dawson came even closer six minutes from time with a shot from 15 yards that rattled the bar.