Nemanja Matic, who was also sent off after being booked twice, crashed home a first-half winner for United to seal Thursday's (AEDT) second leg, but the damage had been done to the Red Devils in the first leg.
City produced a wonderful display in that first meeting at Old Trafford, and was arguably unlucky to win only 3-1, although that proved to be enough to send Pep Guardiola's men to Wembley, despite a frustrated performance in the home leg.
Despite finding itself under extreme pressure at times in the first half, United managed to go into the break ahead thanks to Matic's strike in the 35th minute, casting some uncertainty over City's command of the tie.
But United was unable to use that goal as a launchpad, and failed to craft further meaningful chances and Matic's late dismissal for a second booking effectively ended all hope.
City looked eager to kill off United's chances as early as possible, with Sergio Aguero and Riyad Mahrez forcing David de Gea into fine saves in the first seven minutes.
United weathered that storm and took the lead just past the half-hour mark, Matic slamming a crisp half-volley into the bottom-right corner after Fred's delivery was only partially cleared.
Raheem Sterling seemingly erased United's lead just before half-time when he turned Bernardo Silva's pass home, but the England international had strayed offside.
Sterling had another opportunity in the 58th minute when he was played through on goal, but after checking back to evade Victor Lindelof and then De Gea, he blazed his effort over from 12 yards.
United was reduced to 10 men 14 minutes from time when Matic cynically tripped Ilkay Gundogan to halt a counter-attack, and City had little difficulty seeing out its aggregate win from there despite Aguero's late strike being disallowed for offside.