Captain Richard Naylor's sixth-minute strike was enough to see United claim the points and notch back-to-back Championship wins after victory over Millwall.
The Hornets pushed forward for an equaliser, but they came up against a Leeds defence who were in no mood to give anything away to the delight of Grayson.
"It's a good result because it's our first away win of the season, a clean sheet as well and this is a difficult place to come and get a result," he said.
"Watford have a way of playing, we have to deal with that and show different sides of our game. We passed the ball as well as we can do, although we were not creative as we like to think we can be.
"But we had to show a resilience, defend properly, head things, keeper coming for the ball and catching and we showed a lot of good aspects in terms of our defending.
"When you get the early score, it gives you something to, not hang on to, but it gives you the opportunity to make sure that you try and keep a clean sheet and we did that."
Centre-back Naylor marked his 450th career appearance with the only goal at Vicarage Road.
The 33-year-old was in the right place at the right time early on to prod home the 45th goal of his career after Scott Loach had tipped over Luciano Becchio's header for a corner which Watford failed to deal with. The goal was one of just a few noteworthy incidents, with quality in short supply.
Large parts of the game were spent with both sides trading long balls and, short of a handful of effort from just inside the area, Watford rarely looked like recovering.
There was no place in unchanged Leeds' starting line-up for new signing from Cardiff Ross McCormack, who later forced a save from Loach.
Watford: Loach, Hodson, Taylor, Mariappa, Doyley, Eustace, Cowie, McGinn (Buckley 64), Mutch, Deeney, Sordell. Unused substitutes: Gilmartin, Walker, Jenkins, Bryan, Bennett, Henderson.
Leeds United: Schmeichel, Connolly, Collins, Naylor, Bessone (Hughes 46), Sam (Gradel 60), Kilkenny, Howson, Johnson, Becchio, Watt (McCormack 69). Unused substitutes: Higgs, Bruce, Clayton, Somma.
Referee: J Linington (Isle of Wight).
Man of the match: Richard Naylor.