The visitors had the chance to immediately respond only for Manucho to sidefoot horribly high from 10 yards.
Manucho levelled with a powerful header but Matthew Bates prodded in Tony McMahon's corner to restore the lead.
David Wheater cleared a Manucho header off the line before Marlon King slotted in to secure Boro's win.
Their defender Brede Hangeland is a handful but when Manucho came on it was a different ball game.
Duke played a big part in the win as he again denied Dempsey before Manucho's dramatic late heroics.
Substitute striker Manucho is on loan from Manchester United and Brown hopes he will help Hull steer clear of relegation.
Manucho sidefooted in at the far post from a Richard Garcia cross at the end of a game that Fulham dominated.
Jones missed a cross and needed Wheater to clear Manucho's header off the line, which did nothing for the home side's nerves.
Manucho Barros ended his barren spell to score after eight minutes, but it wasn't enough to stake a place in the last four.
Fagan was in the thick of the action and was forced to clear off the line when a Bolton corner deflected off team-mate Manucho.
The shot did not take a deflection but Hull were awarded a corner from which Barmby headed wide at the far post after Manucho's flick-on.
Despite the setback, Hull did not take long to regroup and exposed Boro's occasional vulnerability in the air when Nick Barmby's cross was converted by loan striker Manucho.
Angola striker Manucho put the visitors ahead in the 33rd minute with a glancing header from Diego Costa's cross but five minutes later Borja Fernandez was red-carded for a lunge on Diego Perotti.
Angolan international Manucho was introduced as a second half substitute by United but headed wide when unselfishly played in by Ronaldo before Berbatov saw an effort cleared off the line by Danny Higginbotham.
Clemente has earned four points from two games since taking over as Diego Costa headed the opening goal four minutes before halftime and fellow striker Manucho scored the second eight minutes after the break.
Craig Fagan was sent through on goal and, after Boro keeper Brad Jones had swatted the ball away from him as he prepared to shoot, Manucho sent the loose ball across the face of goal.
应用推荐