Wednesday took the lead on six minutes when defender Graham Coughlan headed home a Kenny Lunt corner.
Then Nigerian international Akwuegbu had a couple of chances with a volley, which went over the bar, and a header that went close.
The trialist also saw another shot blocked after good work by Tomi Ameobi before Leeds misfit Kevin Nicholls sent an effort just wide.
Wednesday started the second half strongly and doubled their advantage on 51 minutes when David Graham scored with a strike from 25-yards.
The hosts were well clear by the 70 minute when Crockett came racing out of his area but failed to clear the ball, leaving Jason Bradley the easiest of chances to make it 3-0.
The Whites: Crockett, Madden, Crainey, Nicholls, Grace, Wilkinson, Gardner, Howson, Ameobi (Elliott 61), Akwuegbu (Cartman 73), Rothery (Bayly 65).