Moritz Volz's first-half strike was enough to put Fulham through to a fourth-round meeting with Derby after a poor-quality replay at Craven Cottage.
The home side carried most of the threat in the first half and Volz drove home after a pass from Papa Bouba Diop.
Tomasz Radzinski finished well after a pass from Andy Cole as Fulham remained the better side after the break.
Watford failed to trouble Edwin van der Sar until he parried Neal Ardley's fiercely-struck free-kick late on.
The Hornets had hoped to emulate the superb form they have shown in the Carling Cup, but they struggled to make an impression in the first 45 minutes.
There was not much from Fulham either early on, apart from a Zat Knight header from Lee Clark's free-kick which went just over.
But they went ahead when Volz fired powerfully across 40-year-old Alec Chamberlain after Diop's through-ball came off Jermaine Darlington's heel.
Luis Boa Morte came close to a second when his 20-yard free-kick fizzed just over the bar but the game was still short on inspiration, leaving the crowd subdued.
The pattern continued after the break, with Fulham in control of the tie and Watford unable to trouble their defence.
A moment of rare quality saw Cole thread a superb ball through to Radzinski and he finished with aplomb.
Ardley finally gave the visiting fans something to cheer about in time added on but van der Sar dealt comfortably with his effort from the edge of the box.
Fulham: Van der Sar, Volz, Knight, Rehman, Bocanegra, Radzinski, Diop, Clark (Pembridge 63), Legwinski, Boa Morte (John 84), Cole (McBride 71). Subs Not Used: Crossley, Rosenior.
Booked: Rehman, Diop.
Goals: Volz 13, Radzinski 65.
Watford: Chamberlain, Chambers, Demerit, Cox, Darlington, Devlin (Gunnarsson 67), Mahon, Blizzard (Dyer 67), Bouazza (Ardley 67), Webber, Helguson. Subs Not Used: Doyley, Young.
Ref: A D'Urso (Essex).