
The result lifted Watford two places to 18th on eight points from 12 games while Norwich, who last won in September when they upset champions Manchester City 3-2 at Carrow Road, dropped to the foot of the table on seven points.
Deulofeu fired the visitors into a second-minute lead when he robbed Emiliano Bouendia of the ball at the halfway line, cut inside a defender and drove a swerving low shot past Tim Krul.
Gray, who came on for the injured Roberto Pereyra on the half-hour mark, had a shot blocked in the 33rd minute before Bouendia blazed his effort high and wide at the other end.
Spaniard Deulofeu then turned provider in the 52nd when he got a cross in at the second attempt and Gray’s deflected back-heel beat Krul at the near post to double Watford’s advantage.
The visitors had defender Christian Kabasele sent off midway through the second half for a second bookable foul but always looked more likely to score a third on the break as lacklustre Norwich failed to create any chances.