Cole was in top form as Crystal Palace visited West London in a game which would determine which of the two sides is in greater threat of relegation.
Andy Johnson scored to make it 1-1 in the first half, but as Tomasz Radzinski added a third goal late on it became clear that the Eagles now face an even tougher fight to stay up.
Fulham welcomed Luis Boa Morte back from injury, but Palace started brightly almost gained an immediate advantage through young Tom Soares after just two minutes. But after latching on to a long ball over the top by Fitz Hall he shot wide.
But after just four minutes it was Fulham who took the lead. Radzinski turned Johnson brilliantly before picking out Cole in the box.
The Fulham striker took one touch before quickly burying a right-footed shot beneath Gabor Kiraly.
The home side pushed on and could have extended their lead within two minutes, but Steed Malbranque just failed to get on the end of a pass by Boa Morte.
Wayne Routledge proved a threat all afternoon for Crystal Palace and on 11 minutes his neat run and cross should have set up the Eagles leveller.
Tony Popovic headed the ball back across goal and young Soares arrived right on cue, but somehow miscued his header from four yards and put it over the bar.
Fulham began to lose their momentum and the match fizzled out as Palace tried to get a grasp on the game, but it was the home side who did eventually manage to create the next chance.
Malbranque shot wide after Danny Granville half cleared a cross from Cole and then Boa Morte headed wide from a Mark Pembridge corner.
On 30 minutes Palace striker Johnson finally came to life with a diving header which whistled over the bar.
And three minutes later it was the Eagles' top goalscorer who brought them level.
Johnson latched on to a long ball by Hall and Fulham keeper Edwin Van der Sar clumsily brought him down inside the area.
Referee Dermot Gallagher wasted no time in pointing to the penalty spot, and Johnson stepped up to crack home his 11th goal of the season.
With new found confidence Johnson was flying and came close again moments later with an acrobatic overhead kick which flew just over.
Aki Riihilahti soon tested Van der Sar with a fierce drive, while at the other end Radzinski curled in a right-footer which was well saved.
In the second half Fulham upped the pace and on 60 minutes they finally regained their lead through the quality of Cole.
Cole received a pass from Malbranque on the edge of the box and made Popovic and Michael Hughes look amateur as he turned and poked the ball past Kiraly.
Routledge wasted a chance to bring Palace back on even terms almost immediately as he fired over the bar and Fulham continued to look like the side most likely to score again.
Boa Morte was a thorn in Palace's side all afternoon and the Portuguese winger tried to set up Cole for his hat-trick on 64 minutes.
A superb run and pass ended at the feet of Cole, but this time his shot flew over the bar.
Fulham had no need to worry however as they extended their lead on 75 minutes. Malbranque charged down the right and cut the ball back across the six-yard box.
Radzinski arrived right on cue to slide the ball in past a stranded Kiraly in the Palace goal.
Lee Clark emerged for the final ten minutes after nine months out through injury and received a rapturous welcome from the home fans.
Things are now looking up for those supporters down by the river, but over at Selhurst Park they face a tough fight to keep their place in the top-flight.
Man of the Match: Andy Cole – The former England striker netted two goals to guide his side to a crucial victory, taking his tally to nine for the season.