The Mariners came to the East End oozing confidence after five league wins on the trot but found the home side in battling mood.
The Daggers bossed the opening period with striker Ben Strevens coming close in the sixth minute, when he spooned an easy chance over from six yards.
Midfielder Shane Huke also missed an easy chance, firing straight at Grimsby keeper Phil Barnes after racing on to a Jon Nurse pass.
Grimsby midfielder Nick Fenton came close for the visitors in the 23rd minute when his powerful 25 yard volley was saved by Daggers keeper Ed Thompson.
Daggers winger Sam Sloma again should have opened the scoring a minute later, but saw his close range shot clawed away by Barnes.
Former Barnet striker Strevens came close again in the 37th minute when he nodded a Sloma cross over the bar from point blank range.
The Mariners improved in the second half but failed to capitalise on a mixup in the Daggers defence in the 46th minute when Thompson punched thin air after coming for a cross.
The keeper made amends two minutes later when he pulled off a superb save to deny Mariners midfielder Nick Hegarty.
The visitors came close again in the 54th minute but midfielder Paul Bolland fluffed his shot when one on one with Thompson.
Dagenham soaked up the pressure and almost hit Grimsby with a sucker punch in the 56th minute but striker Jon Nurse failed to connect with an inviting Sam Saunders cross.
Barnes kept the scores level in the 60th minute when he stretched to keep out a venomous Saunders volley from the edge of the box.
The Mariners had Barnes to thank again in the 80th minute when he clawed out a Jamie Taylor header from underneath his crossbar.
Grimsby piled on the pressure in search of a late winner but the Daggers held on for a draw.