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It was fast becoming an end to end game as Boro pushed bodies forward and Watford used their pace to make the most of the space left behind, and when the Hornets broke with 10 minutes to go Forestieri put in Dyer who chested the ball and then lifted his shot on to the crossbar.
Beasant, up for a late corner, flicked a header wide of goal in the dying seconds, but it was not to be as Reebok Kendrick Lamar Classic Leather Perfect Split
Watford, though, took the lead moments later, when Forestieri put in Diego Fabbrini who cut inside and teed up Dyer who placed his shot into the back of the net.
their Hertfordshire neighbours went through.
Boro then rattled the woodwork when a ball up to Darius Charles was held up Reebok New Sneakers by the front man, and he nicely teed up Charlie Lee whose sensational hit flew past Jonathan Bond only to smack against the outside of the post.
Capital One Cup first round
Watford then nearly got themselves a second, but this time Beasant got down quickly to save at the feet of Gianni Munari, while at the other end Dembele whipped in a cross from the left and Charles' effort from six yards was kept out by a wonderful reaction stop by Jonathan Bond.
Stevenage made one change from the side that beat Hartlepool United on Saturday, with Jerome Okimo coming in for his first start for the club in place of Jon Ashton.
Watford then went close again, this time Dyer stretching for a ball over the top only to touch it the wrong side of the post with Beasant sent diving the other way.
Stevenage's hopes of overcoming Championship opposition in the Capital One Cup first round for the second successive season have been dashed by Watford.
Graham Westley also adopted a 3 5 2 formation with Okimo and Tom Pett playing as wingbacks with Harry Worley, Dean Wells and Bira Dembele across the back.
Watford: J Bond, Munari, Andrews, Forestieri, Doyley (Ekstrand 29), Tamas, Pudel, Fabbrini (Murray 81), Dyer, Ighalo (Vydra 85), Holban. Subs: Gomes, Doherty, Smith, Johnson.
Boro knocked out Ipswich Town at the same stage of the Saucony Bait Cruel World
It was an encouraging opening half for Boro, carrying over from the win at the weekend, and within three minutes of the restart Lee went close again as Adam Marriott set him up and he curled his effort just off target.
competition last season, but Lloyd Dyer's calm finish for the Hornets shortly after half time meant that it was the visitors who progressed.
Stevenage: Beasant, Okimo (Deacon 56), Dembele, Worley, Wells, Pett (Ashton 80), Whelpdale, Bond, Lee, Charles, Marriott (Calcutt 80). Subs: Day, Johnson.
It was Watford who began the better of the two sides, though, and their first shot at goal came courtesy of Fernando Forestieri who cut inside and curled over when he should have at least tested Beasant.
There was also drama right at the last when Beasant went up for a corner and connected with his head, only to flick the ball agonisingly wide of goal with the full time whistle just seconds away.
Stevenage 0 Watford 1
Boro had their chances as Charlie Lee hit the post, Darius Charles forced a fine save out of Jonathan Bond and goalkeeper Sam Saucony Trail Shoes
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