The Hornets started the game slowly but went in level after Isaac Price and Imran Louza exchanged beauties in the 15 minutes before half-time.
Gracia’s side came out the blocks fast after the break, though, and Vata stroked home after an excellent Marc Bola run to earn Gracia his first victory since rejoining the club.
West Brom dominated possession in the early stages, boasting 93% of the ball seven minutes into the match, but were unable to carve out too many opportunities.
The odd Watford counter-attack came to nothing and it was visitors midfielder Alex Mowatt who struck the first proper effort on goal, shooting wide from distance after 21 minutes.
The Hornets grew into the game a little from there, with Rocco Vata a particular influence on the match, but were soon behind.
After Watford gave the ball away from a goal kick, Isaac Price unleased a superb strike that Egil Selvik could get nowhere near.
Hector Kyprianou and Imran Louza (Image: Alan Cozzi/Watford FC)
The Hornets were soon level with a goal that arguably surpassed it, though.
A loose ball feel to Louza on the edge of the box and he bent a stunner beyond Griffith’s despairing dive to bring his side level just four minutes later.
Watford grew in confidence from there and went closest to scoring again before the break, Vata heading wide.
Gracia made two subs at half-time, introducing Tom Ince and Mamadou Doumbia for Jeremy Petris and Nestory Irankunda.
They wanted a red card when Aune Heggebo caught Hector Kyprianou – and though it wasn’t given, continued to push from there as Louza landed an audacious effort onto the roof of the net.
Jeremy Petris on the ball (Image: Alan Cozzi/Watford FC)
Soon enough, though, they were in front.
Marc Bola did brilliantly down the left to storm away from Campbell and pick out a low cross that was half-cleared as far as Vata, who shot through a crowd of bodies to put his side in front.
That brought West Brom back into the game as a force and James Abankwah produced some exceptional defending to prevent an equaliser, throwing himself in the way as Heggebo looked set to tap in after Selvik saved.
Watford continued to threaten at the other end, though, with Ince forcing Griffiths into action and the excellent Doumbia bending wide as the game entered its last 15 minutes.
From there, the Hornets defended excellently to limit West Brom to nothing and earn a warranted victory.
Watford: Selvik; Ngakia, Pollock, Abankwah, Bola; Petris (Ince 46), Louza (Dwomoh 90), Kyprianou, Vata (Kayembe 72); Kjerrumgaard (Sissoko 88), Irankunda (Doumbia 46)
Unused subs: Baxter, Keben, Morris, Baah