Deeney blasted his spot kicks straight down the middle in the 52nd and 82nd minutes to give the home side a win which leaves them 17th on 34 points with three games to play, six ahead of third-bottom Bournemouth who have a game in hand.
The game began with a minute's silence to mark the passing of former Newcastle and Ireland manager Jack Charlton, who won the World Cup with England as a player, after he died on Friday aged 85. The players also wore black arm-bands in tribute.
Dwight Gayle had put mid-table Newcastle in front after 23 minutes when he steered the ball home after a superb glancing header from a corner by visiting defender Federico Fernandez, which looked to be heading in at the far post.
Deeney had another chance shortly afterwards but his stinging shot was saved by Martin Dubravka, and strike partner Danny Welbeck had a shot deflect off two Newcastle players before looping over the keeper and landing on the roof of the net.
Having come back from a goal down to win 2-1 in midweek against now-relegated Norwich, Watford boss Nigel Pearson praised his team's fighting spirit.
"It doesn't matter how we win at the moment, as long as we do, and this gives us a little bit more of a chance [of staying up]," he said following the final whistle.