Aleksandar Mitrovic scored his 28th goal of the season before the English Championship leaders were held to a 1-1 draw by Blackpool on Saturday.
Mitrovic scored from close range as Fulham dominated early on at Craven Cottage, with Harry Wilson and Fabio Carvalho both coming close to adding a second goal.
The game was halted for over 40 minutes in the first half while a supporter received medical treatment.
Fulham, aiming for a fifth successive league win, were then pegged back in the 57th minute when CJ Hamilton pounced on Tosin Adarabioyo's mistake to set up Josh Bowler for a tap-in after both teams had hit the woodwork.
"It was a disappointing result," said Fulham manager Marco Silva. "We scored a really good goal and had great chances to score the second."
Referring to the delay caused by the supporter's illness, he added: "Then unfortunately we had the break and it was a really serious situation, so all our thoughts are with our friend.
"We were too slow in the second half."
Blackburn remained second in the table following a goalless draw away to Luton. The hosts came closest to scoring when Cameron Jerome struck the post in the 40th minute.
"It wasn't a beauty contest, it was about digging in today, and not making the mistakes that would cost you a 1-0 defeat," said Rovers manager Tony Mowbray.