Everton got off to the perfect start as the ever-impressive Lucas Digne picked out Bernard on the left, the Brazilian cut inside before firing home in just the 10th minute -- his first Premier League goal at Goodison Park.
In response, Watford came close to an equaliser in the 24th minute but Craig Dawson saw his header bounce off the crossbar.
Watford pressed for an equaliser but Everton stood firm to pick up their 10th clean sheet in their last 13 league games and earn Marco Silva a victory against his former club.
"We got an important win," Silva said. "It was important to start winning at home in our first game.
"Keeping a clean sheet is always important even though our mentality is to play offensive football."
Digne missed a chance to score early after dragging his shot wide but then produced a superb long-range pass to pick out Bernard for the opener -- a goal Watford goalkeeper Ben Foster could have done better with.
After Pickford thwarted Deeney's effort with his face, the home fans kept getting frustrated with the team's wayward passing.
New Everton recruit Moise Kean should have doubled the score but he shot wide late on with the goal at his mercy.
"I am disappointed with the result but not the performance," Watford manager Javi Gracia said.
"In my opinion we deserved something. If you don't score in the moment when you dominate the game then you get punished."