Michael Coulson gave the Mariners a deserved first-half lead before Jon Nurse equalised for Jon Still’s men after the break.
Grimsby enjoyed the better of the opening period and took the lead in the 36th minute when Coulson collected a deep cross from fellow loanee Nicky Featherstone before turning inside and lashing a fierce shot past Tony Roberts at his near post.
It could have been two shortly before the break as Peter Sweeney’s curling free-kick came off the underside of the crossbar and onto Adam Miller’s head before bouncing clear.
Dagenham improved after the interval and levelled on the hour when Nurse glanced a header over Nick Colgan.
Paul Benson could have snatched victory for the visitors late on, but he somehow hit the bar from close range with the goal gaping.