Marouane Fellaini’s late header gave Manchester United a two-goal cushion to take into the second leg against a resolute but limited Hull.
After missing variety of opportunities, Red Devils midfielder Juan Mata found the net with a tap following well-delivered head-cross by Mikityran.
Manchester United have not won the EFL Cup, nee League Cup, since 2010 but were seconds away from returning to Wembley three years ago.
It took United 56 minutes to break down a resolute Hull side at Old Trafford, Mata strooping at the far post to turn Henrikh Mkhitaryan’s header beyond Eldin Jakupovic.
United coach faulted the players for celebrating first goal.
“We needed to play,” he told Sky Sports. “In cup ties every goal can be crucial, so why celebrate when you have half an hour to play?
“I don’t think we should, there is no reason to celebrate the first goal.”