Wes McDonald opened the scoring for Blues just ahead of half-time with a powerfully hit shot into the top corner of the net.
The victory was sealed in the second minute of stoppage time at the end of the match when a Wednesday defender deflected the ball into his own goal.
“It probably wasn’t the best performance of the season,” admitted Academy coach Steve Spooner.
“In the first half our football we too predictable, although we did show resilience in not conceding when we under pressure.
“But we were much better in the second half and we created several chances.
“Overall it’s been a good season because we’ve used some very young players and they’ve coped very well individually and collectively and it bodes very well for next season.”