Any prospect of the Championship side producing an upset was effectively over after six minutes, when defender Tim Ream hauled down Gabriel Jesus in the area and was sent off.
Raheem Sterling and Jesus had missed their previous two penalties, but Ilkay Gundogan avoided making it an unwanted hat-trick when he tucked the ball into the corner from the spot.
City – who made eight changes and started with Sterling, Sergio Aguero and Kevin de Bruyne on the bench – soon took total control as Bernardo Silva added a classy second from the edge of the box.
The Portuguese’s effort meant City brought up their century of goals in 37 games, two more than it took last season.
Jesus added two second-half headers, capitalising on poor Fulham defending, for a side who have averaged five goals per game in home FA Cup matches under Pep Guardiola.