The 29-year-old netted his first goal for the Red Devils from the penalty spot in the second half after he arrived at Old Trafford from Arsenal in the January transfer window.
After a goalless first half at Old Trafford, Romelu Lukaku fired Manchester United into the lead in the 55th minute.
And Sanchez stepped up to score his penalty in the 68th minute as he netted his first goal since his move to the Red Devils.
Mourinho has been delighted by Sanchez’s commitment and performances for the Red Devils since his arrival at the club.
And the Portuguese coach was happy with the former Arsenal star’s contribution on Saturday afternoon as Manchester United moved two points closer to Manchester City, leaving them 13 points off the leaders.
Speaking to BBC Sport after the game, Mourinho said: “It was nice for Alexis Sanchez to win a match, the first at home.
“Nice for him to play well and show the desire and happiness in playing football. That is most important. It was not the goal of his dreams, but it is a goal.”
Manchester United will return to Premier League action next weekend when they take on Newcastle United at St James’ Park.
The Red Devils have not won the Premier League since their final triumph under Sir Alex Ferguson back in 2013.
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