Sheffield Wednesday goalkeeper Kevin Pressman saved a penalty and scored one to send the Owls through to the second round of the LDV Vans Trophy.
Pressman blasted Wednesday's second penalty home and then saved Stuart Campbell's effort as the Owls triumphed 5-4 on penalties, following a 1-1 draw after 120 minutes.
Adam Proudlock had netted to take the match into extra time. He volleyed home Michael Reddy's 70th minute knockdown, after good work on the right from Sungu N'Dumba and Derek Geary.
The equaliser came after a sustained spell of pressure from the hosts who fell behind after 90 seconds.
Grimsby caught the home defence cold, striker Darren Mansaram firing low past Pressman after the Owls had failed to clear an Iain Anderson cross.
Reddy was the inspiration for Wednesday as they sought a second-half equaliser. He was off target with a lob in the 54th minute after being fed down the channel by Geary.
Then he tested Aidan Davison on the hour, beating two defenders and forcing the goalkeeper to beat out his shot with his feet.
Wing-back Jon Beswetherick, desperate to impress the fans who booed him at the start, did himself no favours heading wide of an open goal after Davision had failed to claim a Geary cross in the 36th minute.