Watford ended a club record run of 11 successive home defeats and Everton moved a point closer to Premier League safety after a dismal game at Vicarage Road.
Everton had the better openings but were wasteful against relegated and injury-hit Watford, who named former Forest Green manager Rob Edwards as their next head coach before kick-off.
This was an opportunity missed by Everton, with Demarai Gray wasting their best chance by shooting inches wide while Watford keeper Ben Foster saved well from Richarlison's deflected shot.
Everton, however, were aided in their battle to avoid the drop by Leeds United's heavy home loss to Chelsea and now have home games to come against Brentford and Crystal Palace.