Pep Guardiola's side lost on the night but advance thanks to the impressive 1-3 victory at Old Trafford in the first leg.
Nemanja Matic handed the visitors the lead after 35 minutes and just before the interval, Raheem Sterling thought he netted the leveller, only for the linesman to have his flag up for offside.
United's goalscorer was then sent off for his second bookable offence with just under 15 minutes remaining in the second half.
It was a case of Deja Vu for City late in the second period, as Sergio Aguero neatly finished past David De Gea, but the linesman had his flag up for offside once again.
City held their nerve and remained resolute to set up a battle with fellow Premier League side Aston Villa for glory at Wembley in March!
View the best images from the match below.