The Armenia international netted the Red Devils’ first goal in the 42nd minute at the King Power Stadium when he sprinted clear of the Leicester defence and slotted a cool finish past Kasper Schmeichel.
Zlatan Ibrahimovic then made it 2-0 to the visitors shortly after when he drilled home Antonio Valencia’s low cross for his 20th goal of the season.
Juan Mata added a third in the 49th minute at the King Power Stadium as he finished from Mkhitaryan’s through-ball.
But former Liverpool defender Carragher was particularly impressed by summer signing Mkhitaryan’s performance as Manchester United boosted their top-four hopes with victory over the champions.
Speaking during Sky Sports‘ coverage of the game, Carragher said: “The brilliant thing about Mkhitaryan is the pace he’s got.
“How many number 10s in that position have got the pace to get away from someone?
“If that was Juan Mata [for the opening goal] I think Wes Morgan would have caught him. He’s got blistering pace.
“We said before the game that United need to score more goals, they can’t always rely on Ibrahimovic.
“He’s the one who you think can be the man who gets those goals, getting into double figures season after season, playing in that role where he associate him from Borussia Dortmund.”
Manchester United now turn their attentions towards their home clash against Watford at Old Trafford next weekend as they look to continue their push for Champions League qualification.
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