United moved a step closer to Wembley as Marouane Fellaini's late header put the Reds in a commanding position at the halfway point of the semi-final against injury-hit Hull.
A near full-strength United side struggled to break down the determined and resilient Tigers but Juan Mata poked us ahead in the second half before substitute Fellaini nodded home the second to put the Reds in control.
Marco Silva's side had set about with the intention of still being in the tie ahead of the second leg at the KCOM Stadium, and the new boss will have been pleased with his makeshift side's effort and commitment.
Swiss stand-in stopper Eldin Jakupovic instantly found himself called upon when he pushed out Mata's effort from close range after two minutes.
Harry Maguire fired wide for Hull on the counter attack before Antonio Valencia went close from distance at the other end.
Henrikh Mkhitaryan twice lashed off target when he perhaps should have done better, and Paul Pogba then tried his luck with a 35-yarder, only to be thwarted by a superb stop from Jakupovic.
Marcus Rashford had a swerving shot that flew narrowly over, but despite our dominance, it was the visitors who almost claimed a shock lead.
Adama Diomande drifted into space from a Robert Snodgrass free-kick and sent a downward header back off the post, but the flag was raised was an offside infringement.
Intent on killing off the tie as quickly as possible, United upped the ante and raised their tempo after the break.
Wayne Rooney came agonisingly close to breaking the club's goals record on 51 minutes when his low effort on the angle flashed inches wide.
However, the elusive breakthrough was not long in coming as United finally took the lead five minutes later.
Mkhitaryan's header from Valencia's cross looped dangerously to the back post and Mata was lurking to poke home his seventh of the season.
Hull went close to an equaliser against the run of play when David Meyler picked out Diomande, who could only fire over the bar with his acrobatic effort.
Pogba rattled the post with a 20-yard free-kick, and substitute Anthony Martial fired wide as United searched for the all-important second goal.
It duly arrived in the 87th minute when Darmian picked out Fellaini - who had just come on - to steer in a header and put further daylight between the sides.
Jakupovic kept out Martial to prevent a third, but United had long since sealed a ninth successive win (a 15th match unbeaten) and are now firm favourites to reach a first League Cup final since 2010.
Overall team performance: 6.5/10
United Faithful Man of the Match: Juan Mata