Iwobi came on nine minutes into the second half but could not help Fulham claw their way back into the game.
Two quick goals from Mykhailo Mudryk, Armando Broja in the first half sealed the win for the Blues.
Going into the game, Chelsea had failed to win their last six London derby fixtures (losing four and drawing two).
Also Chelsea have now picked up their 150th London derby victory in the Premier League, becoming just the second side from the capital to reach this milestone after Arsenal (151 such wins).
Also Read: I Lost Appetite, Sleep After 1998 World Cup Red Card Beckham
Mudryk scored his first-ever goal for Chelsea when he broke the deadlock on 18 minutes.
Just one minute later after Mudryks opener, Broja made it 2-0.
Chelsea climb up to 11th spot on eight points after seven games while Fulham are 13th also on eight points.