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.
"I'm disappointed with our result. It is probably fair, we haven't been good enough this season," Norwich captain Grant Healy said.
"It's difficult for me to comment on anything right now. Emotions are high, we gave our all but it wasn't enough and the story of our season.
"It's important not to look too far ahead, we still have pride to play for. Then we will see where we stand."