The 27-year-old Pereyra doubled the hosts' advantage soon after the break, driving into the box before curling a neat finish into the far corner from a tight angle.
Watford had 19 shots and could have won by more against a Brighton side who failed to register an effort on target in a disappointing opening-day defeat.
"I’m very happy with the result, but happier with the way we got it," Gracia told the BBC.
"I think we played a very good game, dominated all the game. They didn’t have any shots on target or create any chances. The team showed a good reaction after losing the ball and I am very happy for them.
"I think today we have played the same way (as in) our last game against Sampdoria in pre-season: very aggressive, good attitude and ambition. (I am) very proud of my players."
Watford saw Brazilian Richarlison depart Vicarage Road to join Everton in the summer but captain Troy Deeney said there was enough quality in the squad for them to build on last season's 14th-place finish.
"People thought we would fall apart because Richarlison left, but this is a great squad," he told the BBC. "We’ve got Nathaniel Chalobah and Gerard Deulofeu to come back.
"We had a great start (and) got fans behind us early with our pressing, which is what we aimed to do. We had a great pre-season and it showed with our fitness towards the end, so long may that continue."
(Reporting by Tom Hayward, editing by Ed Osmond, Neville Dalton)
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