Roy Hodgson's Cottagers side grabbed a goalless draw at Bolton Wanderers, but they were fortunate to do so as Kevin Davies' last-gasp header was ruled out.
Replays suggested there was very little wrong with the effort as Davies rose relatively unchallenged in Fulham's penalty area to nod beyond custodian Mark Schwarzer.
- Follow it live from 8pm
After going 12 games without a win, it was lucky 13 for the Clarets as they secured a 2-1 victory against relegation-threatened West Ham United at Turf Moor.
David Nugent's effort opened the scoring before a fine second-half free-kick from new boy Danny Fox settled the contest.
Although the Hammers halved the deficit through their new signing Ilan, the Clarets held out for the win that moved them out of the relegation places.
It is Burnley's home form this term that has kept them out of serious trouble but, on the road, they have collected a demoralising one point from a possible 36.
Fulham sit in tenth place with their home form also bolstering their position and everything points to another away-day disaster for the Lancashire-based club.
Brian Laws knows his team must change the record if they are to avoid an automatic return to the Championship at the end of the campaign.
Hodgson has a number of injury problems ahead of the midweek clash with Zoltan Gera (knee) and Simon Davies (ankle) struggling to feature.
Paul Konchesky (ankle) and John Paintsil (knee) will both definitely miss out as will long-term victims Clint Dempsey (cruciate ligament) and Andrew Johnson (knee).
Laws has five injury concerns but his worries could soon be coming to an end as they are all closing in on full-fitness.