After drawing the first game 1-1, Hull never appeared in any real danger of losing the replay on Monday as they dominated for large periods against their Championship opponents.
Curtis Davies' looping header gave Steve Bruce's side an early lead, and Robert Koren doubled the advantage with nine minutes of the first half to play.
Leonard Ulloa pulled a goal back for Brighton in the 69th minute, scoring his fifth goal in as many games in all competitions.
An improving Brighton pushed for an equaliser to take the game to extra-time but Hull were able to hold on and Bruce will welcome one of his former clubs to the KC Stadium in the next round.
Neither side seriously threatened prior to Hull taking the lead in the 14th minute with a soft goal.
Koren's left-wing corner was met in the penalty area by Davies, whose header looped towards goal and cannoned off the post into the net with Jake Forster-Caskey unable to clear.
Hull's lead was doubled when more poor defending from the visitors saw Koren's free-kick beat Peter Brezovan with the aid of a slight deflection, although Matty Fryatt looked to be in an offside position when the set-piece was taken.
Koren's delivery brushed the outstretched foot of Stephen Ward as the defender looked to clear the danger and succeeded only in changing the flight of the ball to wrong-foot his goalkeeper.
Brighton struggled to find their best form in the first half but started the second with more intensity and went close to halving the deficit within four minutes of the restart.
Ward's cross from the left was not cleared by the Hull defence and Lewis Dunk reacted quickest, only to see his left-footed volley crash against the crossbar and bounce away to safety.
After Hull had wasted two chances to stretch their lead, the visitors punished them for their profligacy as Ulloa pulled a goal back.
The Argentine striker timed his run perfectly to meet a free kick from David Lopez and head past Harper from close range.
Ulloa had a chance to level the game in the closing 10 minutes as he rose to meet a right-wing cross, but the 27-year-old headed over the bar.
Brighton continued to press in search of a late equaliser, but their hopes of staying in the competition were extinguished as Hull maintained their slender lead.
