Watford dug deep to force a replay as Fulham failed to convert superiority into victory at Vicarage Road.
The Premiership visitors took the lead on 17 minutes when Zat Knight headed in a Mark Pembridge cross.
But a penalty, apparently conceded by Fulham keeper Edwin van der Sar in a goalmouth scramble, was then dispatched by Heidar Helguson before half-time.
The Cottagers were then guilty of squandering a series of chances as they pressed forward in search of the win.
Newcastle transfer target Luis Boa Morte was the star of the show for Fulham and was ably supported by Steed Malbranque and John Collins.
But their contributions were insufficient to defeat a spirited Watford side.
And Van der Sar had to repel a stinging drive from Gavin Mahon following an aerial scramble near the end.
Watford boss Ray Lewington:
"It was a cracking match, a fantastic game of football. It's a pity that it has to go to an extra game but you can't pick your matches. A draw was a fair result.
"They will say they hit the woodwork three times and they were a little unlucky but we had more chances in and around the goalmouth - I'm very pleased with the performance.
"We kept going and in the last 20 minutes there was only one team going to win it. There was a bit of character out there. We'll fancy our chances in the replay, although the odds are against us."
Fulham boss Chris Coleman:
"The pitch wasn't great, it was windy, we rode our luck a bit defensively and it could have gone either way.
"But this is the FA Cup and that's the way it goes. In the end a draw was the best result.
"The replay is another game we don't need but I'd rather have it than not be in FA Cup at all."
Watford: Chamberlain, Chambers, Cox, Demerit, Darlington,Devlin (Dyer 82), Gunnarsson, Mahon, Ardley (Webber 66),Bouazza (McNamee 76), Helguson.
Subs Not Used: Doyley, Blizzard.
Goals: Helguson 42 pen.
Fulham: Van der Sar, Rosenior, Knight, Fontaine, Bocanegra,Malbranque, Pembridge, Legwinski (Clark 83), Boa Morte, John,Cole.
Subs Not Used: Volz, McBride, Crossley, Rehman.
Goals: Knight 17.
Ref: A D'Urso (Essex).