The Cottagers started the game brightly knowing that their future among the English elite depended on a good performance against a Blackburn team with an FA Cup hangover.
A Simon Davies corner inside the opening ten minutes was met by a towering header from Senegalese midfielder Papa Bouba Diop which was touched in at the far post by Vincenzo Montella.
Mark Hughes' side tried to get back into the game but it was clear that a third game in six days was taking its toll on them.
Mortern Gamst Pedersen had the first chance for Rovers midway through the first half with a curling free-kick as Antti Niemi did well to get across his goal to make a good save.
Fulham almost gifted Blackburn a way into the game just before the half-hour mark when a lack of communication from Liam Rosenior left Niemi scrambling across his goal to save a header from the defender.
Zat Knight then came to Fulham's rescue when he cleared a Jason Roberts shot that had beaten Niemi.
In the second half it was the visitors that came out of the blocks the faster and Benni McCarthy rattled the woodwork with a powerful 20-yard shot minutes after the re-start. Christopher Samba than had a chance to level but blasted over from 12 yards.
The equaliser finally came just after the hour mark when a good run by Stephen Warnock down the left wing ended with his cross being turned in by the in-form McCarthy - his 21st strike of the season.
Blackburn then set about looking for a winner and created a number of chances as the pace of McCarthy and Roberts kept the Fulham defence busy.
The best chance for a Rovers winner came on 71 minutes when Roberts broke free and held the ball up well. He laid it into the path of his strike partner Roberts, but he could not keep his shot on target.
With tough games coming up against Arsenal and Liverpool, Fulham will be looking nervously over their shoulders at the drop zone while Blackburn's faint hopes of Europe are still alive.