The battle of the ports ended with honours even as Plymouth Argyle failed for the tenth time in the last 12 seasons to mark the opening day with a victory.
The Pilgrims came from behind when Marino Keith equalized Michael Boulding's 28th-minute opener within four minutes, but, after taking the lead through Graham Coughlan four minutes after half time, they conceded a set-piece equalizer just after the hour to Iain Anderson.
Argyle manager Paul Sturrock included David Norris and Jason Bent, at the expense of Steve Adams, and Coughlan, back from injury, in place of Hasney Aljofree.
Grimsby, who flew down to the West Country, contained seven players who did not experience relegation from the First Division last season. The newest was Laurens Ten Heuvel, signed overnight on a short-term deal from Sheffield United.
Two other former Sheffield men also made their bows: right-winger Marcel Cas, formerly of United, and centre-back Tony Crane, ex of Wednesday, alongside goalkeeper Aidan Davison, Jason Crowe, left-winger Anderson; and Des Hamilton, recently of Cardiff.
Argyle fell victim to a sucker punch when Boulding broke to beat Lee Hodges, and shot under Romain Larrieu, but responded almost immediately when Tony Capaldi crossed from the left for Keith to head home.
Paul Wotton's free-kick from the right was rounded off by Coughlan to put the Pilgrims in front, but the points were shared when Anderson fired the ball home from 20 yards following a well-worked corner.