The teams could meet again in the play-offs to reach the Football League, and were that to occur Grimsby would want their goalkeeper James McKeown to match the outstanding form that defied Wrexham until the Welsh side scored all four of their penalties in the shoot-out.
Adrian Cieslewicz, Danny Wright and Chris Westwood scored before Johnny Hunt converted the trophy-clinching spot-kick. Sam Hatton hit the post and Richard Brodie fired over for Grimsby, whose only successful penalty came from Joe Colbeck.
Grimsby had earlier gone ahead in the 71st minute when Colbeck sprinted down the right and crossed to Andy Cook, who saw his first shot parried by Chris Maxwell before sidefooting in when the ball came back to him.
Wrexham levelled with a penalty awarded with nine minutes remaining when Dean Keates was brought down by Shaun Pearson and Kevin Thornton converted.
Former Manchester City junior Cieslewicz was denied by two fine saves from McKeown in extra-time, the first from a 30-yard volley on the turn and the second from a sweet curling strike, and the goalkeeper also repelled a fierce volley from Wright.
Grimsby had faded as an attacking force and that extended into the shoot-out as they missed their first two kicks. The large Wrexham contingent in a crowd of 35,266, and player-manager Andy Morrell, were soon celebrating silverware.