Already trailing 2-1 at the break, the Bantams were sunk by the quickfire brace as their hopes of reaching the fourth round for the first time in 12 years crumbled.
Forsyth’s first goal came on 56 minutes when he latched on to a scuffed shot from Mark Yeates to finish from close range.
His second, just three minutes later, was an altogether more impressive effort as he latched on to a fine through ball from John Eustace to beat Jon McLaughlin from 20 yards.
City did, at least, have the last word on 88 minutes when Nahki Welkls bundled Charlie Taylor’s cross in to give the 1,206 fans in a crowd of 8,935 something to cheer.
Ross Hannah then had the ball in the Watford net in the final minute only for his celebrations to be cut short by an offside flag.
Bradford manager Phil Parkinson said: “We started slow and gave them a goal early, but we responded very well to that and it was a shame we came in at half time 2-1 down.
“It was a good test for us and we had a lot of good things in terms of the two strikers scoring for us which is important.
“It has been a lot of hard work in terms of changing that mentality around, that toughness within the squad. We’ll have a little breather this week.”
Two first-half lapses in concentration at the back meant Bradford City trailed just 2-1 at the break.
The League Two club put in a brave performance in the opening 45 minutes and grabbed a goal of their own through James Hanson.
But they were left to rue the two mistakes that allowed the Hornets to go in at the break ahead.
The tie started at breakneck speed as, first, Watford went ahead and then City hit back, all within the opening eight minutes.
Poor marking by the Bantams defence in the third minute allowed the Hornets to strike first, Troy Deeney afforded so much space inside the six-yard box that he couldn’t fail to head Marvin Sordell’s cross beyond Jon McLaughlin.
It was the worst possible start for the League Two side but they hit back quickly courtesy of a fine finish from James Hanson after Ricky Ravenhill’s shot had initially been blocked by Carl Dickinson.
The rest of the half saw Watford create the better chances.
First, the City goalkeeper held on to a dipping shot from John Eustace and then he kept out a Deeney header after Mark Yeates had got to the byline.
McLaughlin was finally beaten five minutes before the break by Sordell, who was left in far too much space by the visiting defence to finish from close range.
Bradford came closest to adding a second eight minutes before the break when Hanson headed over after Jonathan Bond had failed to collect Robbie Threlfall’s corner.
Phil Parkinson made one change as Bradford City appeared in the FA Cup third round for the first time in eight years.
The Bantams chief has brought Ritchie Jones back in to replace David Syers, who is suspended following his red card against Shrewsbury Town.
Otherwise, Parkinson has stuck with the team that lost 3-0 at Rotherham United in the club’s last outing on January 2.
For the full report and reaction read Sports Monday free inside your Yorkshire Post.