Ings, who came off the bench for Leon Bailey, found Watkins with a searching ball from the left with practically his first touch and his fellow forward capitalised on a slip by Brandon Williams to fire Villa into the lead after 41 minutes.
Ings got on the scoresheet himself in the dying minutes of the match to double Villa's lead with a sharp swivel and shot.
Norwich needed to avoid defeat and hope Burnley did not beat Watford to avoid going down.
However, late goals from Jack Cork and Josh Brownhill gave Burnley a 2-1 win and condemned Norwich to the Championship after one season back in the top flight.
Villa's first win in six games moved them up to 13th, on 40 points, while Norwich are rooted to the bottom on 21.