Roberto Pereyra scored his third goal in as many Premier League games with an exquisite curling effort before Jose Holebas added a seemingly unintentional second from outside the area in a resurgent second-half display.
Palace threatened in the opening exchanges despite their talisman Wilfried Zaha being the victim of a fierce tackle from Etienne Capoue, for which the Watford midfielder was fortunate to receive only a booking.
Zaha did pull a goal back for the visitors late on, beating his marker to drill the ball through Foster's legs, but Watford withstood the fightback to claim all three points.
Watford boss Javi Gracia said afterwards: "I'm very happy because it is always difficult to get a result in the Premier League. We have three wins and it is amazing. The players have been rewarded because they have worked very hard.
"They believe we can do things. At this moment we have played really well the last few games but we know it is very early and only three steps.
"I feel the same as I felt from the first day - I'm very proud to be Watford coach."