The game was goaless at half-time, with the best chance falling to Cleveland Taylor.
His close range effort was tipped over by Aidan Davison.
Grimsby took the lead through Chris Bolder in the 58th minute, but found an equaliser 15 minutes from time.
Paul Hayes forced the ball home after Davison failed to deal with a volleyed shot from Russell Penn.
The match went straight to penalties at the final whistle, with each side missing one of the regulation five spot-kicks.
The pressure got to Dean Crowe who put his effort over the bar, leaving Wayne Graves to seal the win.
Assistant manager Russ Wilcox told the Scunthorpe Telegraph he was delighted with the performance.
He said: "It was pleasing because that was their full first team.
"Everybody showed great bottle for the penalties, we had a mixed side out and played some good football."
Scunthorpe: Evans, Graves, Williams, Kell, Stanton, Ridley, Taylor, Hunt, Hayes, Parton, Featherstone.
Subs: Penn, Capp, Brown, Twiby
Cods: Davison, Crowe, Barnard, Bolder, Crane, Ford, Hockless, Campbell, Jevons, Mansaram, Anderson.
Subs: Soames, Fraser, Hildred, Rowan, Wheeler.