While the point means they are now unbeaten in two matches following a goalless draw at Harrogate Town in midweek, the result against the Mariners means Boro have failed to score in seven outings, an unwanted club record.
Story of the game
However, Alex Revell's side carved out a number of openings, with their first early chance their best, as Elliott List's cross from the right channel was met by Marcus Dinanga, whose effort was blocked by visitors keeper James McKeown.
Ian Holloway's side responded with a Virgil Gomis long-range shot that flew wide for Grimsby.
Keen to banish the memory of their 2-0 defeat at the hands of Leyton Orient last time out at the Lamex, Boro were committed and lively throughout an energetic first half.
Following the interval, Boro extended their dominance with a brace of chances to go ahead, but List's shot in a crowded box flew over - before the impressive Charlie Carter's header was deflected the wrong side of the post for the home side.
As the clock ticked down, Stevenage forced two late saves from the alert McKeown, the second of which denied Aramide Oteh's curler, as both sides shared the spoils with a point apiece.
Stevenage remain in 21st place ahead of their trip to Colchester on Tuesday.
Takeaways from the game
In case you hadn't realised from watching this match, Stevenage right-back Luther James-Wildin is a class act. A superb talent allied with an excellent technique and top notch temperament. His athletic performance against the Mariners showed just why he was linked with Premier League giants Arsenal a couple of seasons ago. Destined to play at a far higher level.
Boro boss Alex Revell deserves sympathy - and time
Former Stevenage striker Alex Revell always gave his all in Boro colours as he did throughout his career which spanned nearly two decades in the lower leagues. So, despite, Stevenage's disappointing run of seven matches without a goal, it was good to see his side play with verve and vigour against an obdurate Grimsby side led by the canny Ian Holloway.
While he and his charges will rue the chances they failed to convert it can only be a matter of time before his side score a hatful of chances. With Concorde Rangers next up at the Lamex a week today, home fans will hoping Revell's side finally open the floodgates. On this showing it won't be long.
If the 22-year-old QPR loanee does half as well as last year's temporary Loftus Road attacker Ilias Chair, he will have done well. Interesting to watch former Rangers boss, now Grimsby manager, Ian Holloway, deep in conversation with him after the match.
Man of the match: Charlie Carver
While many observers considered Luther James-Wildin to have been the standout performer against Grimsby, the sponsors gave the award to an equally deserving recipient in Charlie Carver.
His boss, teammates and fans alike will be delighted to have him back in the side following a spell on the sidelines. The creative talent was unlucky not to score with an early shot but will be pleased with his excellent performance. Keep an eye on this lad.