Adam's first-half header, which hit a post before rebounding into the net off Hornets keeper Heurelho Gomes, secured a deserved three points for the visitors.
Hughes was forced to reshuffle his team with Ryan Shawcross, Phil Bardsley and Glenn Whelan out injured and Joe Allen suspended.
But Adam and recalled record signing Giannelli Imbula bossed the midfield in Allen's absence while Glen Johnson and Marc Muniesa slotted in seamlessly at the back.
Stoke climbed into the top half of the table and host Burnley next weekend with Adam predicting some tough decisions for the boss.
"It was an excellent performance," he told the club website. "We had a few key players missing but the lads who came in were excellent and it's the manager's headache next week.
"We knew Watford would come at us in the first half but we were excellent all game.
"That's the character you have to show when you're not playing. When you come into a team that's playing well you have to stamp your authority.
"It's a headache for the manager next week but it's a good one to have. It's nice to see us in the top half. It was a great away performance and we'll move on to Burnley at home."