'AGT' Contestant Dr. Brandon Rogers' Audition Airs After Death

"America's Got Talent" contestant Dr. Brandon Rogers was a gem of a talent before his tragic death ... as you can see in his audition episode, which just aired.

Dr. Rogers' family wanted the audition to run, showing the young doc humbly taking the stage only to wow the crowd and all 4 judges with a fantastic cover of Stevie Wonders' "Ribbon In The Sky."

He gets a standing O from the judges -- even Simon Cowell.

We broke the story ... Rogers was killed in a car accident last month after his friend fell asleep at the wheel and veered off the road.