Gary McSheffrey had Scunthorpe's first real opportunity of the match when he picked the ball up 20 yards from goal and curled a shot just wide of the post.
Wilbraham then saw a glancing header saved before McSheffrey struck the post for Scunthorpe with an effort from just outside of the box.
City eventually got the breakthrough when Luke Freeman's deep corner was met by Flint at the back post after the break.
His powerful downward header put City in front despite Miguel Llera's best efforts on the line.
Scunthorpe's Niall Canavan had a header cleared off the line at the other end before substitute Cunnigham sealed the win for City by smashing the ball into the top corner.