Ilkay Gundogan gave the Blues the lead from the penalty spot when Tim Ream was sent off for trucking down Gabriel Jesus as an ingenious dummy by David silva sent the striker clear.
Bernardo silva doubled their lead when he pirouetted on the edge of the area before firing into very cheap corner – making city the first team in Europe’s top 5 leagues to succeed in a hundred goals altogether competitions this season.
In the last half, pep Guardiola’s side threatened additional goals, as substitute Raheem Sterling hit the bar before an incredible tackle from Fulham debutant Terence Kongolo stopped Jesus when clear through.
The Brazil striker eventually got his goal once he met a Joao Cancelo cross to go past keeper Marek Rodak.
He made it four, 163 seconds later, once he reacted fastest to a saved Phil Foden effort to nod into an empty net.
The fifth-round draw is on Monday twenty seven January.