The London club had only scored three goals away from Craven Cottage this term, but Bolton gifted Andy Johnson, Simon Davies and Diomansy Kamara three more as Roy Hodgson's side wrapped up the points.
Kevin Davies' 11th goal of the season had cancelled out Johnson's first-half opener following Andy O'Brien's blunder.
And Simon Davies and Kamara punished further mistakes from the hapless O'Brien and Gavin McCann to boost Fulham's hopes of a UEFA Cup spot.
After a dull first 29 minutes, the game finally burst to life when Gary Cahill, twice, and then McCann contrived to miss from close range after Mark Schwarzer failed to hold Johan Elmander's free-kick.
Fulham had hardly threatened, but only a brilliant save from Jussi Jaaskelainen stopped the visitors from taking the lead after the big Finn reacted magnificently to deny Bobby Zamora on 38 minutes.
Johnson himself then failed to take advantage of more slack marking inside the Bolton penalty area and his mis-hit volley was headed clear by Cahill.
But the striker made no mistake three minutes before half-time after being gifted the opening goal by O'Brien. Bolton were in no real trouble until the defender's poor first touch took the ball away from goalkeeper Jaaskelainen and into the path of the grateful forward, who slid home his tenth of the season.
Fulham looked to be heading into the interval with a deserved lead until Kevin Davies struck in first-half injury time.
The Bolton captain exchanged passes with Mark Davies, nutmegged Paul Konchesky with his first touch and swept the ball past Schwarzer.
The Cottagers keeper made a fine save to keep out Elmander's volley after the club record signing latched on to Kevin Davies' lob seven minutes after the restart.
But it was Hodgson's side who grabbed the crucial goal on 56 minutes and once again it was O'Brien badly at fault.
The Irishman was robbed by Johnson wide on the left and though the former England slipped, Murphy was in support. The midfielder's first effort was blocked before he rattled the crossbar with his follow-up attempt.
The ball rebounded to Davies, who beat Jaaskelainen and Jlloyd Samuel's last-ditch clearance on the line.
Kamara had only been on the pitch four minutes when McCann inexplicably passed the ball straight to Clint Dempsey, who squared for the substitute to add a third late on and spark wild celebrations among the travelling fans.