Speculation over Jol's future at the club has been rife following a poor start to the season that has seen them win only three games so far, leaving them in the bottom half of the Premier League.
Fulham have not tasted victory over United since 2009 and were behind early on as Antonio Valencia was handed the easy task of tapping in from close range after Wayne Rooney had cleverly sucked in goalkeeper Maarten Stekelenburg.
Robin van Persie doubled the lead as he latched on to a ball from Januzaj before rifling in at the near post.
And a first-half rout was completed when Van Persie supplied Rooney for another simple finish as United made it 10 goals in their last three games in all competitions, highlighting their continued improvement under manager David Moyes.
Alexander Kacaniklic's deflected strike gave Fulham hope midway through the second half, but that proved to be nothing more than a consolation.
United made five changes from the side that beat Stoke City 3-2 in their last Premier League outing, Adnan Januzaj deployed on the left wing in place of Shinji Kagawa, while Nemanja Vidic was restored to the defence.
Striker Darren Bent was dropped for Fulham as Iranian midfielder Ashkan Dejagah was handed his first league start of the campaign.
It took United just nine minutes to break the deadlock as Valencia slotted into an unguarded net following neat link-up play from Van Persie and Rooney.
Moyes' men continued to dictate play following the goal, but Fulham twice had chances to level matters as David de Gea denied Dimitar Berbatov from close range.
The hosts were made to pay for their profligacy, though, Van Persie emphatically slamming the ball past Stekelenburg after 20 minutes following a deft pass from Januzaj.
And United put the game beyond all doubt a mere two minutes later as Van Persie turned provider for Rooney after dubiously being ruled onside from Phil Jones' throughball.
Fulham made an improved start to the second half and came close to pulling one back when Pajtim Kasami's long-range effort flew just past the right-hand post.
United went close through substitute Marouane Fellaini, but Fulham did pull one back 20 minutes into the second half as Kacaniklic cut inside to unleash a fierce effort that deflected off Rooney, leaving De Gea no chance.
Substitute Bent hit the bar from close range late on but Jol's men never looked like mounting a miraculous comeback as United moved just two points shy of the top four.
