A dull opening 30 minutes was livened up by a sprinkling of gold dust by both sides' liveliest first-half performers.
The Baggies were rewarded in the 34th minute with an impressive strike by Price. Mikey Johnston's left-wing pass was dummied by Aune Heggebo and, in doing so, it presented Price with the space and time to lash home a 25-yard right-footed shot into the top corner.
The visitors' advantage lasted just four minutes, as Louza collected possession and struck a beautiful looping shot over the head of Josh Griffiths into the top right-hand corner.
Louza was to dominate for the rest of the night as Watford emerged as the sharper team after the break, and the Hornets did not have long to wait for their second goal of the night.
The tenacious Marc Bola outpaced and outmuscled Albion substitute George Campbell, sending in a low cross from the left. Nat Phillips stumbled over the ball and the half-clearance fell for Vata, who drove the ball through a crowded box to hand Gracia's side the lead.
Price had a chance to restore parity for Albion just after the hour mark following good work by Alex Mowatt, but the Northern Ireland international's 63rd-minute header was saved by Egil Selvik, with Heggebo unable to convert the rebound.
That was as good as it got for Ryan Mason's visitors.
Striker Daryl Dike was thrown on for his first appearance of the season, but the visitors were unable to draw level, so Albion remain without a win at Vicarage Road since 2007.