United then scored a superb team goal as Wayne Rooney found Jesse Lingard before the England attacker laid it off to Pogba who fired home a stunning strike in to the top corner for 3-0 in first half stoppage time.
Mourinho's team scored all their goals between the 31st and 48th minutes, starting with a penalty apiece for Paul Pogba and Anthony Martial, and either side of that period they did not really have to extend themselves too greatly.
Kjaer was culpable again, as Rooney intercepted his misplaced pass and crossed to Lingard, who showed great awareness to tee up Pogba for a marvellous first-time finish into the top-left corner from 20 yards.
Mkhitaryan, a big-money summer signing from Borussia Dortmund, has not played since the derby loss to City on September 10.
"I am lucky to be here to work in the Premiership and I want to work every day to prove I belong here because I want to stay for a long time", said Mourinho.
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He added: "It is three points and that is what we needed".
"And then probably because Martial was the one that had the previous action and Martial also is a good penalty taker, they made that decision, it's not a problem for me".
"We are a football-playing side and Manchester United were more physical and stronger than we were with a lot of tall players", said Klopp. "I am not an Einstein, ..."
"I'm really happy. It's quite attractive for me to meet him, I don't know, five or six years later [after being his manager at Inter Milan], and see the same ambition, passion and desire to play and compete". He knows what he wants and the levels are high, so he always wants to keep up the pressure.
Three minutes later they were two up thanks to another penalty, this time won and converted by Martial, who ran onto a fine ball from Mata before being pushed in the back by Sener Ozbayrakli. I only bring the players [to the press conference] that are going to start. I am never happy to concede a goal. Am I happy with individual performances? Yes. "We knew after the first defeat (1-0 at Feyenoord) it was important to get nine points at home and a few more away, so it was a very important victory for us". "To go to Istanbul without winning this match would be even more hard".