United's defeat means City are 10 points clear with both sides having three games left to play.
United's win put on hold the title celebrations of champions-elect Manchester City.
Fans stormed the stadium and pitch before kick-off in protest against the club's owners - the Glazer family.
The 47-year-old is charged with causing actual bodily harm to a woman in her 30s and common assault of a woman in her 20s, as well as one count of coercive and controlling behaviour between 2017 and 2020.
Villarreal face Arsenal in the other semi after the Gunners thrashed Slavia Prague 4-0 away to complete a 5-1 aggregate victory.
United edged their heavyweight tie with AC Milan as Paul Pogba came off the bench to score the goal that secured a 1-0 win in the San Siro for a 2-1 aggregate triumph.
United won thanks to an early penalty from Bruno Fernandes and a second-half strike from Luke Shaw with the result narrowing City's lead at the top of the table to 11 points over United with 10 games remaining.
United became only the second team to win a Premier League game 9-0, matching their 9-0 win over Ipswich Town in 1995 and also Leicester City's away rout of Southampton in 2019.
Chelsea's fifth defeat in eight matches dropped them to eighth place, nine points behind the leaders.
A superb second-minute lob by Danny Ings gave Southampton a surprise 1-0 home win over leaders Liverpool.