The Iron's tie against Newcastle United had gone to extra-time on Thursday night, and with most of the players who went through that 120 minutes playing again less than two days later it is little surprise they were slow out of the blocks.
Striker Gary Madine gave Wednesday a fifth minute lead, bundling the ball home from close range after meeting Lewis Buxton's low cross.
Controversy followed moments later when referee James Linington reversed his initial decision to award Scunthorpe a penalty - following David Prutton's challenge on Chris Dagnall - after consulting one of his assistants.
Ben Marshall put Wednesday further ahead in the 17th minute with an angled effort which was deflected into the roof of the net.
It took more than an hour for the Iron to get a foothold in the game. The lively Dagnall struck a post before Bobby Grant pulled a goal back in the 67th minute, tucking the ball neatly past Nicky Weaver from inside the area.
Madine grabbed his second goal of the game three minutes later when he slotting the ball past the advancing Josh Lillis after being put through on goal.
Iron substitute Mark Duffy scored five minutes from time to set up a tense finish, but Wednesday held on to win.
Source: DSG