Despite Bruce making nine changes, the Tigers were always too good for a below-par Boro who displayed none of the verve they had exhibited during their successful festive period.
Aaron McLean's tenth-minute opener ensured the Teessiders were on the back foot from the off, and they rarely looked getting back on level terms before Nick Proschwitz extended the visitors' lead shortly after the hour mark.
Aitor Karanka made six changes to the Boro side that drew with Bolton on New Year's Day, with Dimi Konstantopoulos, Jozsef Varga, Dean Whitehead, Emmanuel Ledesma, Marvin Emnes and Luke Williams all coming into the starting line-up.
Hull boss Steve Bruce made nine changes in his initial selection, and a further alteration was enforced shortly before kick-off when Proschwitz replaced the injured Matty Fryatt in the starting XI.
The unexpected switch did not adversely affect the visitors, however, as they started brightly as took the lead with the game's first attack of note in the tenth minute.
Boro conceded possession in their own half, George Boyd rolled the ball to David Meyler, and while the former Sunderland midfielder's shot was blocked by George Friend, the ball broke kindly for McLean to prod home in the area.
It was the striker's first goal since he scored against Boro for Ipswich last February, and the strike was aided by Konstantopoulos' slow reactions, with the former Hartlepool goalkeeper taking an age to leave his line after the ball broke free in the area.
With a previously untried midfield line-up taking time to settle, Boro never really looked comfortable throughout the first half.
Curtis Main was too isolated up front, and Emnes is particular was extremely profligate in possession, repeatedly losing the ball despite minimal pressure from the Hull defence.
It took Boro 39 minutes to record a shot on target, and even that was an extremely tame affair with Ledesma drilling in a 30-yard strike that did not trouble former Newcastle goalkeeper Steve Harper.
Two minutes later and Main had his first sight of goal, but the youngster slashed at a shot that flew well wide.
Aitor Karanka was clearly unimpressed with his side's first-half efforts, and the Spaniard made two alterations at the break with Lukas Jutkiewicz and Albert Adomah replacing Luke Williams and Ledesma.
The changes had a positive effect, with Boro starting much more brightly after the interval. Jutkiewicz's increased muscularity posed a different question to the Hull defence, and Adomah's dribbling ability meant Maynor Figueroa was unable to push forward from the full-back berth as he had in the first half.
George Friend lashed a speculative long-range shot wide, before Boro spurned their best chance of a leveller shortly before the hour mark.
Figueroa made a complete hash of clearing Emnes' low cross, but Dean Whitehead wastefully shot wide from the edge of the area after he was presented with an inviting shooting chance.
The chance proved to be as good as it got for Boro, as three minutes later, Hull scored a superbly-worked goal to double their lead.
Paul McShane passed to George Boyd, and after he cut the ball back in the area, Proschwitz lashed a ferocious first-time finish into the roof of the net.
The goal took much of the wind out of Boro's sails, although Rhys Williams headed Leadbitter's free-kick over the crossbar under a considerable amount of pressure with 20 minutes left.
Middlesbrough (4-2-3-1): Konstantopoulos; Varga, R Williams, Gibson, Friend; Leadbitter, Whitehead; Ledesma (Adomah 46), Emnes (Butterfield 83), L Williams (Jutkiewicz 46); Main.
Subs (not used): Ripley (gk), Richardson, Hines, Smallwood.
Hull (4-4-2): Harper; Rosenior, Faye, McShane (Chester 76), Figueroa; Boyd, Meyler, Quinn (Jahraldo-Martin 83), Gedo; McLean (Elmohamady 80), Proschwitz.
Subs (not used): Jakupovic (gk), Fletcher, Fryatt, Sagbo.