The Magpies, desperate to get back to winning ways, began the encounter brightly and were first to fashion chances against the Hornets.
Marco Silva's side were shaky at the back and relied on goalkeeper Heurelho Gomes to bail them out on a number of occasions but, with the Magpies so toothless in front of goal, the Brazilian was rarely threatened.
On the stroke of half time, Rafael Benitez's charges were left with a mountain to climb as Zeegelaar sent a cross into the Newcastle box which DeAndre Yedlin bundled into his own net to put the Hornets two goals up.
Although the hosts regrouped and launched several attacks, they continued to flounder in the final third, and were caught out again at the back just after the hour as Andre Gray slotted past Rob Elliot from close range after Richarlison crossed from the left.
Benitez sent on Mikel Merino, Aleksandar Mitrovic and Ayoze Perez in the second half, but Newcastle never looked like getting even just a consolation as the visitors saw the game out without too many issues.
Newcastle (4-4-2): Elliot; Yedlin, Lejeune, Clark, Manquillo; Ritchie, Shelvey, Diame (Merino 69'), Murphy (Perez 77'); Gayle, Joselu (Mitrovic 69')
Watford (3-5-2): Gomes; Mariappa, Kabasele, Britos (Prodl 52'); Femenia, Hughes (Carrillo 84'), Doucoure, Cleverley, Zeegelaar; Richarlison (Pereyra 79'), Gray