The Seagulls were hammered 6-1 at Anfield on Sunday but showed their resilience by extending their unbeaten league run to eight matches despite the Tigers' dominance at the KC Stadium on Wednesday night.
Manager Gus Poyet made four changes, handing a debut to Manchester City loanee Abdul Razak, while Nick Barmby made just one following the 0-0 draw at Birmingham, winger Cameron Stewart replacing Aaron Mclean.
The City boss saw his side start much the brighter as Matty Fryatt's trickery on the right wing allowed him to whip in a cross for Stewart, who took Peter Brezovan out of the equation with a neat sidestep but could not squeeze his shot past Adam El-Abd on the line.
The tireless running of lone striker Craig Mackail-Smith earned Brighton a free-kick almost from nothing in the 10th minute and Kazenga LuaLua fired narrowly wide.
Robbie Brady's ambitious overhead kick from the edge of the box was only ever going to be handling practice for Brezovan but it was at least on target, unlike Mackail-Smith's copycat attempt shortly after, which left the former Peterborough forward in a heap as the ball spun away to a grateful Paul McKenna.
James Chester's well-timed challenge on Ashley Barnes two minutes later looked an ill-advised intervention when the ball broke fortuitously for Mackail-Smith, but his effort was parried away by Vito Mannone.
The foraging runs of Stewart caused the Seagulls problems in the first half and his teasing cross almost picked out Robert Koren just after the half-hour mark, but he was eased out by an alert Joe Mattock.
Brighton's threat was most apparent on the counter-attack and when LuaLua surged forward and his heavy touch inadvertently fed Liam Bridcutt, scorer of two own goals in Sunday's heavy reverse, the midfielder's low drive was only gathered by on-loan Arsenal goalkeeper Mannone at the second attempt.
Still it was the Tigers creating the more inviting openings and another chance arrived moments later as Stewart raced on to a long punt over the top but his attempted chip was blocked and he lost control of the loose ball as it ran to safety.
They were almost made to pay five minutes before the break when the 19-year-old Razak forced a smart stop from Mannone.
The lively Stewart still found time to strike the top of the bar with an 18-yard thunderbolt as the hosts finished the half on top.
When both Fryatt and Brady went close early in the second half it appeared as though the home side would continue to control proceedings, but Mackail-Smith's powerful run, at the end of which he just failed to pick out Barnes in the box, provided a stark reminder Poyet's charges were still in the contest.
Stewart snatched at a shot and put it wide while Chester showed a similar lack of composure when Koren's set-piece delivery arrived at his feet four minutes later.
Substitute Mclean should have won it 12 minutes from the end but he skied over the bar from close range after more good work from Koren.
And, as in October when the two met at the Amex Stadium, the contest ended without a goal as Hull missed out on the chance to climb into the play-off places despite making it six games unbeaten in the league.