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.
Alexander Kacaniklic's deflected strike gave Fulham hope midway through the second half, but that proved to be nothing more than a consolation.
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.
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.
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.
