Wolves enjoyed a comfortable first half after taking the early lead with Wednesday’s much-changed squad unable to threaten Wolves keeper Jose Sa.
Harry Gray supplied the Owls with their best chance of the match after being tripped by Boubacar Traore just outside the box.
The 17-year-old’s direct free-kick was well hit but easily held by Sa before Olagunju nodded in the second for Wolves in first-half stoppage time.
Both sides introduced starters from their league campaigns in the second half after making eight changes apiece to their starting XIs, but neither set of substitutes managed to impact the match.
Doyle provided the first hint of threat after half-time for the visitors, having an effort ripple the side netting before Wolves substitute Raul Jimenez headed Adam Armstrong’s cross wide.
Louie Barry then came closest for Wednesday after a sharp pass from fellow substitute Barry Bannan but his shot from distance drifted over the bar.
The Owls duo continued to link up well but could not fashion a shot to test Sa as Wolves saw out the tie to reach the third round.