The visitors were impeccable in defence and outstanding on the break, with Dempsey scoring a beautiful free kick and a close-range header to put his side 2-0 up at the break.
Mahamadou Diarra then popped up 10 minutes from time to score a third, but only an energetic performance by Adam Bogdan in the Bolton goal stopped the visitors racking up a huge score.
Fulham, safe from the drop but well off the pace for a European spot, have little to play for except pride at this stage of the season, but Damien Duff's man-of-the-match performance will get Ireland fans excited as Euro 2012 begins to come into focus.
Bolton, however, will be furious with themselves for blowing a golden chance to pull clear of the drop zone on a weekend when their relegation rivals all faced tough trips away from home.
Owen Coyle's side were full of confidence heading into the match on the back of three consecutive league wins, seemingly determined to make full use of the kind hand dealt them by the schedule against one of the top flight's worst sides away from home..
But Fulham made that form - and Coyle's Manager of the Month award - look ill-deserved as they pulled all the strings right from the off.
As early as the fifth minute the visitors almost opened the scoring as Bryan Ruiz beat a poorly-run offside trap, and only a brave charge out of goal from Bogdan saved the hosts from conceding.
Bolton were sparked into life by the close call, and spent the remainder of the half pressing forwards at every opportunity.
The Fulham defence was impeccable, however, closing every door, and of the Bolton forwards only Martin Petrov on the left flank consistently managed to create openings.
David N'Gog was also lively, if not exactly focused, and his pass to Ryo Miyaichi on the quarter-hour mark gave a great chance for the Japanese teenager to score. Instead, he merely managed to blast over from 10 yards out.
Fulham have struggled away from home all season, but you would never have known it as they continually soaked up the pressure and came forward on the break.
Duff in particular was outstanding, bamboozling the hapless Marcos Alonso on the right flank, and the Irishman almost created an opener on 24 minutes when his blocked shot fell to Dempsey. The American lashed home, but the flag was up for offside.
Six minutes later there was no flag to get in the way: a rash challenge by N'Gog gifted Fulham a free kick 25 yards out, and Dempsey curled a delightful free kick into the top corner. Bogdan did brilliantly to get a hand to it, but the placement of the ball was simply too good for it to be stopped.
And just before the break another counter-attack gave Fulham a 2-0 lead, however, as Duff again outwitted Alonso and delivered a brilliant cross that looped over Bogdan and allowed Dempsey the luxury of heading home from point-blank range.
Bolton came out fighting in the second half, with the introduction of subs Kevin Davies and Chris Eagles offering them a new attacking edge.
And Eagles went close within minutes thanks to a lovely curling free kick that just drifted wide of the top right corner.
But when Bolton failed to find a breakthrough they soon lost the initiative. Fulham, rather than sit back on the lead, actually began to increase their control of the game.
Duff forced Bogdan into a stunning diving save just before the hour mark after again beating Alonso, a move which sparked a flurry of chances at either end.
The best of these fell to N'Gog, who looked through on Schwarzer until John Arne Riise charged across to make a desperate sliding tackle that saved a certain goal.
Within 60 seconds at the other end Dempsey almost made it a hat-trick as his one-two with Ruiz allowed him a chance of a thundered left-foot shot that just went wide of the post.
Immediately after that Duff again forced Bogdan into another good save.
Bolton, in truth, never looked like scoring, with sub Ivan Klasnic wasting the best late chance with his terrible control of a good pass from Petrov.
And the points were put beyond doubt when Riise broke up the left, cut inside unmarked and delivered a perfect ball across the six-yard box that Diarra slid home to complete a great day for Fulham, and a miserable defeat for the hosts.