The USA international started the ball rolling in the first half with a superb strike, hooking in a half-cleared corner into the top corner.
Dempsey then nabbed his second of the evening three minutes after the break to see him become Fulham's top scorer in the Premier League era, his 33rd strike taking him past Steed Malbranque and Brian McBride before Brede Hangeland stooped in to head home the Cottagers' third.
The victory extended Fulham's unbeaten run at Craven Cottage to seven matches, during which they have picked up 19 points out of a possible 21.
Fulham's last home defeat came at the hands of West Ham on Boxing Day, which left them facing a potential relegation battle.
However, tonight's victory has pushed Mark Hughes' side to ninth in the table, all-but securing Premier League survival in the process.
Heading into the game, skipper Danny Murphy shook off a dead leg to start for the Cottagers who were able to include Philippe Senderos in the squad for the first time since he joined from Arsenal last June.
Bolton's Owen Coyle was forced to shuffle his pack after Daniel Sturridge, who scored his seventh goal in nine games in the win over Arsenal, failed to overcome injury.
The visitors started the stronger and were unfortunate not to break the deadlock within the opening minute.
Kevin Davies' pass from the right found Johan Elmander, whose neat turn and pass was flicked on by Matt Taylor to Fabrice Muamba, who somehow missed from six yards out.
The chance seemed to snap the home side into life, with Jussi Jaskelainen forced into a low save from Dempsey's low drive two minutes later.
The United States international was also heavily involved in the next action of note, providing a neat pass across the box that Eidur Gudjohnsen somehow managed to scuff over the bar.
Dempsey's excellent start continued and he soon broke the deadlock, superbly rifling home a half-cleared corner into the top corner.
The 15th-minute volley was almost followed up minutes later by a second, although this time the midfielder could not keep his shot down.
Carlos Salcido was the catalyst in the latter move and the Mexican had a chance of his own in the 20th minute, cutting in from the left before unleashing a shot just wide of the top corner.
Despite the home side's dominance, Bolton proved dangerous on the counter-attack and Elmander was unfortunate not to connect with a low Chung-yong Lee drive.
Fulham returned to the attack undeterred and Moussa Dembele forced Jaaskelainen into a superb sprawling save as the home side moved from defence to attack with ease.
Gudjohnsen then almost atoned for earlier fluffing his lines by racing onto Chris Baird's superb long-range pass, but the former Bolton man could only rattle his shot against the post.
Bolton right-back Gretar Steinsson saw a fierce drive well held by Mark Schwarzer on the half-hour mark, before Dembele and Hangeland came close for the home side.
Fulham's superb first period could have been tempered just before the break when Tamir Cohen found space to rifle a goalbound shot from eight yards, but Schwarzer held the ball to quell the home faithful's fears.
Hughes' side started the second period in similarly impressive fashion and almost doubled their advantage through Dembele's 22-yard drive, which was deflected onto the bar and out.
The home side did not have to wait long for a second, though, as Dempsey tapped home Gudjohnsen's flick-on in the 48th minute.
The Fulham onslaught continued and, after Simon Davies saw a shot well-blocked by Zat Knight, the third came from a set piece.
Murphy's pinpoint free-kick was met on the penalty spot by Hangeland, whose header flew into the top right-hand corner with 25 minutes remaining.
Bolton came close to grabbing a consolation goal through a Gary Cahill header that flew just wide, before the Londoners thought they had netted a fourth through Bobby Zamora.
Davies' whipped-in cross from the right was well controlled by the substitute, allowing the striker to smash the ball into the top right-hand corner.
However, referee Anthony Taylor chalked off the goal for handball and handed Zamora a yellow card for his troubles.
Bolton continued to attack in the final 10 minutes in search of a goal but were continually thwarted by resolute Fulham defending, with woeful efforts from Steve Sidwell and Elmander the last noteworthy action.