Pep Guardiola included the likes of Kevin De Bruyne, Gabriel Jesus and Leroy Sane in his starting XI, but teenagers Phil Foden and Diaz were the ones to really catch the eye in a straightforward outing at the Etihad Stadium.
City made light work of Fulham in the first half and were unlucky to not add further goals to Diaz's early opener, as they wasted numerous opportunities.
Diaz doubled his tally just after the hour and City subsequently eased to victory, but De Bruyne's late withdrawal may give Guardiola some cause for concern.
Fulham struggled to get out of their half in the first period and Diaz put City ahead 18 minutes in, his close-range effort deflecting past Sergio Rico.
Danilo then went close, clattering a shot against the right-hand post from a tight angle in the box.
Sane should have done better just after the half-hour mark, blasting a half-volley well over from a decent position after an intricate move involving De Bruyne and Foden.
Jesus also failed to find the net on the stroke of half-time, Rico tipping his 18-yard effort wide.
City's dominance showed no sign of abating after the break and Jesus nodded just wide early on from a rare accurate Sane cross.
Jesus went even closer in the 65th minute when Rico nudged his effort on to the post, but Diaz was there to slam home his second of the day.
City suffered the blow of losing De Bruyne to an apparent knee injury late on after a tangle with Timothy Fosu-Mensah, but the Belgian walked off unaided and the hosts booked its passage regardless, with Leicester City or Southampton its next opponent.