As half-time loomed, De Bruyne sent a wicked cross in from the right but Foden’s header went just the wrong side of the far post.
City were straight back on the front foot to start the second half, with Jesus heading wide before De Bruyne’s curling shot went just the wrong side of the post.
They had to wait until the 65th minute for the second goal to come as Diaz netted again.
Leroy Sane slipped the ball through to Jesus, but when his shot across goal was touched on to the woodwork by Rico, it fell for Diaz, who took a touch before lashing home.
Fulham never threatened to stop City keeping a fifth successive clean-sheet in all competitions.
A comfortable evening for the Premier League leaders finished on a low note five minutes from full-time when De Bruyne went down in pain after falling awkwardly in a clash with Timothy Fosu-Mensah.