Andy Johnson opened the scoring with his first away strike in Fulham colours following an error by Bolton defender Andy O'Brien.
The normally travel-sick Cottagers bossed the first period, but it was all square before the interval when Kevin Davies scored his 10th goal of the season right on the brink of half-time.
But Roy Hodgson's side continued to dominate the Trotters and the points were sealed when first Simon Davies gave the Cottagers the lead again with a close-range strike, then substitute Diomansy Kamara added a third late on with Gavin McCann at fault this time.
It was Fulham's first win away from Craven Cottage since the final day of last season and lifted them eight points clear of the relegation zone.
A second successive defeat leaves the gap between Bolton and the bottom three at just four points.
FluencyBoth sides had gone into the game on the back of disappointing losses and they struggled to get any fluency in the early stages and it took until the 28th minute for the first goalscoring opportunity.
Brede Hangeland was penalised for pushing Kevin Davies and from the resulting free-kick Bolton should really have scored.
Johan Elmander's low strike was partially saved by Mark Schwarzer but Gary Cahill followed up with two efforts only to be denied by the goalkeeper and then Brede Hangeland from close range with Gavin McCann eventually firing wide with the goal at his mercy.
Matt Taylor had the ball in the net in the 37th minute after drifting in from the right but he was marginally offside.
Seconds later Jaaskelainen was called upon to make his first save when Zamora controlled Paul Konchesky's left-wing cross 10 yards out but shot straight at the goalkeeper.
However, Jaaskelainen was powerless to stop Fulham's next attack in the 42nd minute as O'Brien tapped Simon Davies' through ball past his own goalkeeper.
The defender chased back but could not prevent Johnson sliding in at the far post to score only Fulham's fourth away goal all season.
However, the hosts were back on level terms in injury time when Kevin Davies chested down a long punt to Mark Davies who returned the pass to the striker and he jinked his way into the area and fired home.
Second-halfWithin five minutes of the restart Murphy's ball inside Jlloyd Samuel put Bobby Zamora clear on the right and his cross seemed destined for the unmarked Johnson until Mark Davies got back to intervene.
However, O'Brien's miserable afternoon continued in the 56th minute when he was robbed by Johnson.
Although the striker was dispossessed as he ran into the penalty area the ball fell to Murphy whose left-foot shot cannoned back off the crossbar.
The rebound dropped to Simon Davies and his shot back across goal could not be kept out by Samuel as the ball just crept over the line.
Cahill flashed McCann's 68th-minute corner wide before Mark Davies, who appeared to injure his knee when Clint Dempsey fell on him, was replaced by Fabrice Muamba.
Bolton upped the tempo in the closing 10 minutes but they struggled to deliver the final ball and the Reebok Stadium crowd became increasingly angry.
With three minutes to go the hosts' misery was complete when McCann's aimless ball into midfield was picked up by Dempsey who played in for substitute Kamara to slot home.
1st Half Goals
Shots on Target
Shots off Target