Zlatan Ibrahimovic missed out because of illness, while Wayne Rooney started but was left to wait for the goal that will make him the club’s all-time leading scorer.
United got off to a bright start when Mata lashed a shot goalward in the second minute, but Hull keeper Eldin Jakupovic was alert to make a diving save to his right.
Hull, dealing with a rash of injuries of late, started with only six men on the bench and needed to use one of them after Markus Henriksen was injured after a quarter-hour following a collision with Paul Pogba.
United escaped a scare after the half-hour mark when Adama Diomande’s soft header struck the post, before the offside flag belatedly went up.
Five minutes after the break, Rooney came close to finding his record breaker when he ran onto a long pass from Pogba and fired inches wide of the post.
The breakthrough came in the 56th minute when Antonio Valencia’s cross found Henrikh Mkhitaryan at the back post, and the Armenian headed back across for Mata to score.
Rooney’s night ended soon afterward as Jose Mourinho withdrew him in favour of Anthony Martial.
United remained in full control, and Pogba hit the post from a free kick, before Jesse Lingard and Marouane Fellaini came on as subtitutes for Mkhitaryan and Mata.
The lead was doubled with three minutes to play after Martial stayed with the ball under pressure from Hull defenders and fed the ball to Matteo Darmian, whose cross to the back post fell for Fellaini to head in and put United in full control ahead of the second leg.
Hull’s injury woes got even worse in stoppage time as Josh Tymon limped off and was replaced by former United midfielder James Weir.