Charlton Athletic lifted some more of their gloom as the relegation-threatened second-tier side won 2-1 at fellow Championship outfit Sheffield Wednesday to end hopes of a Sheffield derby in the last eight.
Davies scored Hull's opening goal with a looping header from Koren's corner in the 14th minute as the Premier League team dictated play.
Koren then added a second in the 36th minute when his free kick - via a deflection from Keith Andrews - beat Peter Brezovan in the visiting goal.
Second tier Brighton managed to halve the deficit in the 68th minute through top scorer Leonardo Ulloa, who also scored in the 1-1 draw in the initial tie last Monday, but they struggled to carve out any more meaningful opportunities.
Hull host boss Steve Bruce's former side Sunderland in the quarter-finals while Charlton face a trip to third tier Sheffield United with the ties to be played March 8-9.
Arsenal host Everton and ManchesterCity welcome holders Wigan Athletic in a repeat of last season's final in the other matches.
Charlton, who sit in the Championship relegation zone, beat promotion chasing Queens Park Rangers on Saturday and the momentum that result provided continued on Monday as they dominated the early proceedings at Hillsborough.
Callum Herriott opened the scoring for the visitors in the 22nd minute when his swerving strike nestled in the top corner.
Leon Best equalised for Wednesday in the 57th minute, converting from close range, but Simon Church restored Charlton's advantage when he nodded home Johnnie Jackson's free kick eight minutes later.
Wednesday had chances to force a replay, with the initial tie postponed because of a waterlogged pitch, but Londoners Charlton held on.
Image: Yannick Sagbo of Hull City celebrates scoring their first goal with Curtis Davies and George Boyd.
Photograph: Mike Hewitt/Getty Images
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