Stoke, who were without a victory in their last five league matches, took the lead when Charlie Adam's corner fell at the near post and Shawcross swept home left-footed deep into first-half stoppage time.
Four minutes after the restart, Crouch followed up his goal against Chelsea on Saturday to score in successive Premier League appearances for the first time since February 2015.
Stoke moved up to 11th on 24 points, two ahead of 14th place Watford.
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It ended a disappointing run for Hughes's side who had conceded four goals to both Liverpool and Chelsea in their last two games and looked in danger of being sucked into the relegation battle.
"We have played better and been beaten in recent weeks, we got goals at good times and then saw the game out quite comfortably," Hughes said.
Watford, however, are now without a win in their last five, having scored just twice and conceded 10 in those matches.
"We have to keep going and give everything for the next match," Watford boss Walter Mazzarri said.
"Nothing is going our way, so it is just a period we are not lucky but we need to change this."
(Reporting by Toby Davis; editing by Greg Stutchbury)
