A combination of standard cup rotation and a sickness bug in the Hull camp meant manager Steve Bruce made nine changes to the side beaten by Liverpool on New Year's Day, but they were still good enough to condemn Aitor Karanka's side to a 2-0 defeat.
McLean, just a day after returning from a loan spell at Birmingham, prodded home his first Hull goal in 15 months after 10 minutes and Proschwitz finished emphatically on the hour to seal it.
Neither man features in Bruce's long-term plans and both could be gone by the end of the month, but their efforts ensured a cup run remains possible for their team-mates.
Of those, George Boyd was the standout - starting the move that led to the opener and adding an assist for the second in an impressive all-round performance.
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 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 David Meyler, whose hopeful shot took a kind deflection and bobbled dangerously behind the defence.
That left debutant goalkeeper Dimi 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 edge of 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 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 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 got 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.
His pinpoint cross was headed into the side-netting by Main in injury-time but that was as close as the Teessiders got.