Having already beaten Sheffield United and Sheffield Wednesday, the visitors thought they had snatched an early lead at Glanford Park when Marc Richards had the ball in the net after only two minutes only to be flagged offside.
Scunthorpe then took charge and dominated the game from start to finish.
Twice they were denied by the woodwork in the first half with Paul Hayes and Michael O'Connor both seeing shots come back off a post.
The home side shrugged off the loss of goalkeeper Joe Murphy through injury after 23 minutes, with rookie Sam Slocombe coming on to make a fine debut.
Scunthorpe pressed forward strongly in the second half with wave after wave of attacks as they strove to break the deadlock.
But with leading marksman Gary Hooper on the sidelines through injury, they could not find their finishing touch in front of goal.
Grant McCann, Jonathan Forte and O'Connor all saw efforts whistle just wide.
And midfield man Matthew Sparrow saw his effort brilliantly turned away by goalkeeper Chris Martin.
In the final minutes of normal time the visitors might have snatched an unlikely winner when full back Kris Taylor had a shot cleared off the line.
But it was Scunthorpe who finally made the breakthrough in the second minute of extra time when a shot from O'Connor was deflected by Hayes beyond the reach of keeper Martin.
Four minutes later, Scunthorpe's place in the last 16 was sealed when McCann danced his way into the box to beat Martin with a good finish.
Forte and substitute Martyn Woolford might have added to the score, while at the opposite end rookie keeper Slocombe pulled off a couple of good saves to deny Vale even a consolation goal.