Striker Andre Gray scored against his former club after just three minutes, before Burnley pegged the Hornets back.
However, goals from captain Troy Deeney and midfielder Will Hughes ensured that Watford walked away with a first Premier League away win since November 2017 and the maximum return of points from their first two games.
Gracia praised his players in the post-match press conference, saying: "Today we scored three and we have done better than last season, but I don’t like to look back at last season, I prefer to enjoy the moment. We did a good job and I’m happy for the players.
"It is important the amount of goals but the quality as well. Today the strikers Troy Deeney and Andre Gray scored which is very important for them and the team. Will Hughes scored an outstanding goal, I am happy for all of them.
"All the players are working a lot, Troy for example has a brilliant attitude every training session, this we will try to keep that in the next games.
"I think we started well, scoring early but after that we suffered a corner kick, it is difficult to defend Tarkowski. In the second half we took a step forward, created more chances.
"You always expect the best, but in this moment I prefer to focus on the next game, the best mentality to do our best."
Watford face Crystal Palace at Vicarage Road in their next Premier League match, as Gracia's men look to make it three wins from three.