Goalkeeper James McKeown saves Christian Nanetti's last-minute penalty as Grimsby hold on to share the points with Dover.
Braintree Town record their first victory of the Conference season against Dover Athletic at Cressings Road Stadium.
A second-half Scott McManus strike earns Halifax victory and ruins Dover's return to the Conference.
Conference Premier newcomers Dover Athletic complete the double signing of striker Jake Reid and defender Sean Francis.
Fixtures, Results & Competitions
Dover Athletic sign former Havant & Waterlooville midfielder Christian Nanetti on a free transfer.
Dover Athletic's Liam Bellamy, Barry Cogan and Lee Hook sign new one-year deals with the Conference Premier newcomers.
Promoted Dover sign former Gillingham forward Stefan Payne, who scored 31 goals for AFC Hornchurch in 2013-14.
Dover Athletic beat Ebbsfleet in the play-off final to return to Conference Premier for the first time since 2002.
Ben Reeves' strike ends non-league Dover's FA Cup run and earns MK Dons a place in the third round.
Amy Fearn becomes the first female to referee an FA Cup match as Dover beat Corby in a first-round tie.