Grimsby lost ground on Conference Premier leaders Luton after sharing a point with Lincoln.
Sean Newton's free-kick was headed past his own keeper by Aswad Thomas and just two minutes later Bohan Dixon picked up his second yellow card for Lincoln.
Grimsby levelled before the break when Craig Disley finished Scott Neilson's neat pass but struggled thereafter.
Grimsby's Lenell John-Lewis was later sent off for his second bookable offence as the game limped to a draw.
VIEW FROM THE DRESSING ROOM
Grimsby Town manager Paul Hurst told BBC Radio Humberside:
"I was happy with how the team performed in general - that was more like us, we passed the ball a lot better, in difficult conditions.
"First half, we got the ball down and played well, it was frustrating that we scored an own goal, but we knew that free kicks and long throws were going to cause danger.
"It ended up 10 v 10 which, you know, looking at it, I think had one of theirs not been sent off, it wouldn't have been a sending-off for our player."
Grimsby Town 13 McKeown 06 Doig 05 Pearson 03 Thomas 15 Bignot 18 Thanoj 07 Colbeck (Rodman - 74' ) 08 Disley 11 Neilson 17 Hannah 14 John-Lewis Dismissed after an earlier booking Substitutes 23 Rodman 24 Walker 20 Southwell 09 Cook 26 McLaughlin Lincoln City 01 Farman 02 Miller Booked 23 Brown 03 Newton Booked 27 Foster 19 Nolan Booked 04 Jordan 17 Dixon Dismissed after an earlier booking 16 Robinson (Everington - 89' ) 09 Rowe Booked 11 Tomlinson Booked (Fairhurst - 86' ) Substitutes 25 Simmons 15 Gray 31 Preece 22 Everington 07 Fairhurst
Ref: Darren Handley