Liam Hearn scored his 27th goal of the season as Grimsby came from behind to extend their unbeaten run to 15 games.
After an undistinguished opening period, Braintree went in front in controversial circumstances.
The referee overruled an offside flag waved by his assistant, allowing Sean Marks to roll the ball home.
Hearn levelled after Nathan McDonald saved Shaun Pearson's header and the visitors hung on for a point when Craig Disley had a shot hacked off the line.
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Grimsby Town joint-manager Rob Scott told BBC Radio Humberside:
"I don't know what interpretation there is of the goal. On the one hand you can say that on their advantage it came off Craig Disley's leg and put the lad in.
"In our defence the lad is offside and when does he not come into play?
"He's offside, he's made a run into our box and he's offside by 10 yards. He comes out with his hands in the air and then the ball ricochets off.
"He's obviously influencing play because he picked the ball up and scored. I asked the fourth official and he said he didn't know."