David Meyler and Maynor Figueroa were the only survivors from their defeat to Liverpool on New Year's Day - but Bruce's second string still had too much for a disappointing Boro side.
The opener came just nine minutes in, with Aaron McLean scoring his first Hull City goal for nearly 15 months as he prodded home ahead of debutant Dimi Konstantopoulos in the Boro goal.
The second goal came on the hour as Nick Proschwitz fired into the top corner to finish off a neat footballing move from the Tigers as they booked their place in the fourth round.
So, whilst Bruce will not be too enthralled with another game in the fourth round, he will be delighted with his fringe players who turned in a very good performance albeit against a fairly abject Boro outfit, who managed just a couple of shots on target in the whole game.
The first few minutes saw Hull begin brightly, Stephen Quinn keen to get on the ball in his first appearance in almost two months due to hamstring trouble and Gedo looking to test Jozsef Varga down the Middlesbrough left.
It took them little time to find the net, with George Boyd the driving force.
The Scot hassled Emmanuel Ledesma as he lingered on the ball 10 yards outside his own box, winning possession and squaring to Meyler, whose hopeful shot took a kind deflection and bobbled dangerously behind the defence.
That left Konstantopoulos and McLean challenging to meet the loose ball and the striker won, poking into the top corner from close range.
It was a belated first of the season for McLean, including seven games with Birmingham, ending a drought that stretched back to February, when he netted against the same opposition during a loan stint at Ipswich.
Meyler went down in some pain as his team-mates celebrated, a result of a collision with George Friend, but Hull's concerns were allayed when he returned to the pitch after a short break.
The goal did little to alter the flow, with Hull enjoying the bulk of possession without seriously threatening a second.
Boro, meanwhile, were struggling to get lone striker Curtis Main in the game with moves too often breaking down before play reached him.
A mistake almost opened the door for Hull in the 33rd minute, Rhys Williams' ill-conceived back-pass heading straight to McLean, but Ben Gibson made a fine covering challenge at the crucial moment.
The home side threatened another self-inflicted wound soon after when Williams appeared to push Gedo inside the box, but referee Kevin Friend saw nothing untoward.
Half-time saw Boro boss Aitor Karanka make two changes, replacing Ledesma and the anonymous Luke Williams with Albert Adomah and Lukas Jutkiewicz.
They certainly came out after the break looking sharper and George Friend signalled his side's intent inside a couple of minutes when he charged Meyler off the ball and struck a powerful shot wide of the near post.
Ten minutes later, Marvin Emnes charged at the Hull defence and drilled a teasing ball low across goal.
A touch from Main would have been enough to turn it home but he was a yard short.
Adomah retrieved it on the byline and found Dean Whitehead, but with a full sight of goal he was both high and wide.
The Boro resistance was cut short on the hour when Proschwitz put the finishing touch on a neat counter down the right wing.
Liam Rosenior and Paul McShane got things going with some tidy interplay that freed up Boyd to race to the byline and cut a pass back to the centre.
The ball arrived slightly behind Proschwitz but he was still able to launch a powerful finish past Konstantopoulos.
Adomah offered pace and flair to Middlesbrough's attack, making his original omission something of a head-scratcher, but he was not able to get them on the scoresheet.