The Magpies had gone into the game without a victory on their travels in seven matches in all competitions, but Fabricio Coloccini's header after four minutes got them off to the perfect start.
The advantage was doubled by Andy Carroll five minutes after the restart and although Will Hoskins gave the Hornets hope with an injury-time strike, it was too little, too late for the home side.
Watford actually had the better of territory and possession in a game lacking in goalscoring opportunities, but the quality of their final ball was often poor against an organised defence superbly marshalled by Coloccini.
The visitors took the lead when a free-kick from the left and level with the edge of the penalty area was not dealt with. Carroll headed back across goal for Coloccini to beat Scott Loach at his near post with a header from inside the six-yard box.
The Hornets responded well to the early setback and had the better of the first half, but struggled to create anything of note for the remainder of the opening period against the visitors' organised defensive ranks.
Watford's hopes of getting back into the contest were severely dented within five minutes of the restart when, from the visitors' first corner of the match. Danny Guthrie clipped the ball towards the near post and Carroll thumped a header past Loach.
The Hornets never gave up though and their efforts were rewarded in injury-time when a Heidar Helguson shot appeared to be blocked by Kevin Nolan's hand, but the ball broke nicely for substitute Hoskins to confidently beat Steve Harper.