The three points will offer a timely boost for manager Frank Lampard as he aims to haul his team back into the race for Europe in the coming weeks.
It was visitors that dominated things in the first 45 minutes with only the woodwork and Alphonse Areola keeping them out before the break.
Mason Mount was inches away from putting Chelsea in front, as he spanked a volley off the bar, before Areola produced a fantastic stop to deny Antonio Rudiger.
And with Chelsea growing in confidence before half time their cause was helped even further as Antonee Robinson was dismissed for a lunge at Cesar Azpilicueta.
Lampard’s team continued to boss it after the break with Areola again called into action to deny Hakim Ziyech and Jorginho.
But with Chelsea continuing to ramp up the pressure on Fulham’s overworked back line, Mount eventually conjured up a breakthrough.
Ben Chilwell’s cross was only half cleared out by Areola and Mount stayed cool to steer home through a crowd of Fulham defenders.
Under fire German international Timo Werner should have made it 2-0 in added time but he dragged poor effort well wide of the post.
Full Time at Craven Cottage it’s Fulham 0 Chelsea 1