Gray scored with five minutes left — his first goal since the win at Leeds in November — before Wade Elliott added a late third.
Akinbiyi had earlier marked his return to the side by scoring the opener.
But it was Gray, fully recovered from a broken bone in his foot, who drew the most praise from a beaming Steve Cotterill.
The Burnley manager said: "Andy Gray is one of the top strikers in the League.
"He is intelligent, brave and does all the horrible work.
"I'm pleased with him because he does all the work and is a top professional.
"I'm pleased for both him and Ade Akinbiyi. They have had rough times this season and come through them."
Norwich went close to taking an early lead when Dion Dublin cracked a fifth-minute volley against the bar.
But Akinbiyi made his former club pay when he rose to reach Michael Duff's cross to open the scoring for Burnley.
Gray put the game beyond doubt by following up after James O'Connor's shot hit the post, and Wade Elliott added a late third from Jon Harley's left-wing cross.
Norwich manager Peter Grant was unhappy with the officials, saying: "I would have been seething even if we had got a point with that performance, and to lose 3-0 is hard to accept.
"We were outstanding but it was very difficult playing against 14 people.
"The officials were awful."
This news has been published by title Andy Gray May Return To Champions League Football With BT Sport... As Michael Owen Is In Hot Water Over Newcastle Liverpool Snub
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