Grimsby Town goalkeeper Ian McKeown produced a magnificent point-blank save to deny Wrexham a second Blue Square Bet Premier win of the season.
McKeown threw himself in front of Chris Westwood to save the Wrexham defender's diving header from four yards after an uneventful 60 minutes.
The keeper then saved Rob Ogelby's 18-yard effort in injury time.
Anthony Elding wasted two openings for Grimsby, who failed to capitalise on Jay Harris's late sending off.
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Wrexham manager Andy Morrell told BBC Radio Wales:
"It was probably a fair result. I'm delighted with a clean sheet because it's been a long time coming.
"I thought we defended really well, and even when we were outnumbered a couple of times late in the second half I thought we coped well.
"So that's the positive from the game."
Grimsby Town joint-manager Paul Hurst told BBC Radio Humberside:
"Coming to Wrexham, who are a team who are expected to be up there, it's a good point for us.
"A 0-0 and a second clean sheet in a row is a pleasing aspect for us.
"The only disappointment was when they went down to 10 men I felt we still sat behind the ball a bit too much instead of trying to squeeze onto them."
Wrexham 01 Mayebi 03 Ashton 06 Riley 18 Walker 23 Westwood 07 Cieslewicz (Ogleby - 80' ) 08 Harris Dismissed after an earlier booking 12 Keates 16 Hunt Booked (Little - 73' ) 10 Ormerod 11 Morrell (Wright - 65' ) Substitutes 13 Coughlin 14 Clarke 17 Little 09 Wright 15 Ogleby Grimsby Town 13 McKeown 02 Hatton 03 Thomas Booked 05 Pearson Booked 22 Pond 04 Niven Booked 07 Colbeck Booked 08 Disley 11 Artus (Chanoj - 81' ) 09 Elding (Southwell - 89' ) 18 Pearson (Cook - 60' ) Substitutes 16 Ford 19 Wood 21 Chanoj 12 Cook 20 Southwell