After a heavy 4-0 loss to Liverpool last time out, Fulham were hoping to revive their league fortunes, having fallen into the relegation places with just three victories to their name.
They fell behind just after the hour, however, when Alejandro Pozuelo's driven low delivery created confusion in the Fulham backline, and in particular Aaron Hughes, who inexplicably tapped into his own goal.
Fulham responded quickly as the excellent Scott Parker lobbed Michel Vorm in fortunate circumstances, but substitute Jonjo Shelvey's excellent late effort condemned Fulham to yet another defeat.
It was the Welsh side's first victory since October 19 and one which looked unlikely as the managerial shake-up at Craven Cottage began brightly, with new head coach Rene Meulensteen's arrival looking to complement Jol.
Darren Bent perhaps should have put the hosts ahead in the first half, with two chances on the half-hour mark as both sides looked solid early on.
The on-loan striker's first chance was put on exquisitely by Parker, whose sumptuous chip played him in, but he could only skew his header wide.
Just four minutes later, an optimistic long ball was pumped forward towards the Swansea defence. Chico was first there to deal with it, but he misjudged his header, placing it instead into the path of Bent who smashed his effort against the post.
Berbatov tried an audacious scissor-kick on the turn in the opening minutes, albeit from an offside position, and Pajtim Kasami, one of few bright sparks in their poor start, felt he should have had an early penalty.
Fulham continued to press for an early goal and centre-back Fernando Amorebieta impressively hooked an effort over his shoulder, which may have looked unnatural but was close to the returning Vorm's goal.
Play soon swung the other way, with Roland Lamah hitting wide and Wilfried Bony failing with a header before Pozuelo robbed the ball off Derek Boateng and played through Nathan Dyer. The diminutive winger looked set to score with a fierce low strike, only for Maarten Stekelenburg to make a wonderful save with his feet.
Swansea continued in the ascendancy after half-time and Bony showed excellent poise and control, before lashing across the face of goal.
Their dominance finally paid off when Pozuelo's low ball in was turned into his own net by Hughes.
It was nearly two soon after as Swansea broke forward, with Pozuelo again the creator but Dyer was denied by a late block.
If there was a touch of fortune about Swansea's goal, however, Fulham took it a step further with the equaliser.
A corner was played short to the influential Parker, who was captaining Fulham for the first time. The midfielder clipped the ball into the area but misjudged the delivery, and it lofted over the waiting players - including Swansea goalkeeper Vorm - to nestle into the corner of the net.
With time running out and Fulham looking to hold on to a vital point, Swansea continued to battle forward in the hope of snatching a first league victory for a month.
It came on 80 minutes. Substitute Shelvey burst forward through a previously solid Fulham defence to curl a great effort past Stekelenburg, leaving the home side rooted in the relegation places and putting manager Jol under yet more pressure.
It was a sucker punch for Fulham and one they were unable to respond to, despite ramping up the pressure in the closing stages.
It was no surprise, therefore, to hear 'Jol out' chanted by many, with only a late Steve Sidwell block preventing the scoreline getting even worse in stoppage time when Shelvey took the ball past Stekelenburg.