The Cottagers went into the game seven points adrift of safety and in desperate need of a win, but two Glenn Murray goals inside the opening 20 minutes left them in dire straits with the Seagulls seemingly on course for a win in snowy conditions in west London.
However, boss Claudio Ranieri’s half-time team-talk clearly had the desired impact as his side stormed back to secure the win thanks to Calum Chambers, a brace from Aleksandar Mitrovic and Luciano Vietto.
The win keeps Fulham 19th but they are now five points off safety while Brighton sit in 13th on 26 points.
Fulham were unchanged from the team defeated 2-1 by Tottenham in their last Premier League outing, while Mat Ryan replaced David Button in goal for Brighton's only change to the XI that lost 2-1 at Manchester United in their last league game.
The visitors enjoyed a dream start when they took the lead in the fourth minute when Martin Montoya was allowed to race away down the right flank before delivering a superb cross which Murray met at the near post before guiding his header into the far corner past Sergio Rico.
Fulham responded positively to falling behind but they failed to trouble the Seagulls’ goal before going two-down after just 17 minutes.
Denis Odoi failed to clear a cross into the area and when Pascal Gross’ overhead kick sent the ball back into the box, Murray was on hand to convert from six yards.
The hosts’ first real effort of the game came on 32 minutes when Ryan Babel exchanged passes with Mitrovic and lashed a strike in from 25 yards which Ryan did well to parry wide of his goal.
Both sides had chances to add to the scoreline in the 38th minute when Murray headed a Gross cross into the back of Odoi and then saw his close-range effort from the rebound saved by Rico.
At the other end Andre Schurrle met a Babel cross into the area on the volley and his on-target effort was blocked on the line by Shane Duffy.
Brighton were inches away from going 3-0 ahead on 42 minutes when Davy Propper hit a rising effort from 25 yards out which beat Rico but smashed off the crossbar.
Fulham were back in the game two minutes into the second half when Duffy headed a cross into the Brighton area back out as far as Chambers and he smashed a first-time volley back into the net from 25 yards.
The goal visibly lifted the Cottagers and it was no surprise when they equalised on 58 minutes after Mitrovic got to a Babel cross back into the area ahead of Duffy and Ryan before heading the ball in from six yards out.
It was all Fulham and they were inches away from going ahead on 67 minutes when substitute Vietto sliced his attempted volley into the path of Jean Michael Serri and he watched as Ryan was at full stretch to tip his effort onto the post.
Brighton then responded with Solly March hitting an effort straight down the throat of Rico on 70 minutes, before Montoya picked out Murray in the area and his header was heading for the net only for the Cottagers’ keeper to brilliantly push it away.
Back came Fulham to complete their comeback on 74 minutes when Joe Bryan chipped the ball into the box and Mitrovic climbed above Duffy before guiding his downward header past Ryan.
And it was 4-2 five minutes later when Tom Cairney watched his 20-yard strike bounced down off the crossbar and, while Babel made a mess of his shot from the rebound, the ball fell to Vietto who slammed it into the net.
Cairney went close to a fifth on 82 minutes but once again the midfielder watched as his strike hit the woodwork before Mitrovic put one over the top when through on goal in stoppage time.