After a first half of few clear-cut chances, Everton came out strongly after the break and Richarlison’s deflected shot forced a fine save from Ben Foster.
Demarai Gray, who looked lively throughout, fired wide from the edge of the area as the Toffees continued to press. But they could not find a winner.
Frank Lampard’s side remain 16th but are now two points above the relegation zone, after 18th-placed Leeds United lost 3-0 to Chelsea on Wednesday.
The Toffees also have a match in hand on Leeds, and a far better goal difference.
Despite Watford’s first home clean sheet of the season, they stay 19th on 23 points.