The best chance fell to Wolves striker Leon Clarke, who fired wide with the goal gaping after Bakary Sako had hit the post in the first half.
There were early half-chances for both sides in west London; Cauley Woodrow fired over from the edge of the box after a good move from the hosts, before Sako’s low strike was smothered by Fulham goalkeeper Marcus Bettinelli.
Clarke had a golden chance to put Wolves ahead after half an hour after Sako’s effort from distance crashed off the post, but the striker shot wide with the goal at his mercy.
At the other end, Hugo Rodallega’s spectacular overhead kick landed on the roof of the Wolves net, before another acrobatic effort from the Colombian fizzed just past the post.
Wolves got off to a good start in the second period, with Lee Evans testing Bettinelli before Sako fired wide from a corner.
But Manchester City loanee Seko Fofana did his best to open the scoring for Fulham, lashing just over from outside the penalty area after a good run, and Woodrow flashed the ball across the face of the box moments later as Fulham pressed hard.
Bettinelli then had to be on guard in the Fulham goal to fingertip a James Henry header over his crossbar from Matt Doherty’s centre, and he then did well to parry wide an effort from Henry, who had robbed defender Shaun Hutchinson.
Excellent footwork from Sako in the latter stages of the game gave him a chance to let fly with Bettinelli stranded, but the ball arrowed inches wide of the goal.
Fulham nearly grabbed a last-gasp winner, but Wolves goalkeeper Carl Ikeme stood tall to keep out Fofana after he was released one-on-one.
Progress to the fourth round will now be decided in a replay at Molineux, where manager Kenny Jackett will be without star turn Sako, with the winger heading off to the Africa Cup of Nations with Mali.