The striker put in a man-of-the-match performance and typified Dagger's robust performance. His goals, aided by strikes from Mark Arber and Paul Benson, moves the East Londoners up to seventh in the League Two table.
It might have been different had Mariners' winger Peter Till not sliced his shot just wide of the target after only seven minutes.
Instead, it was the Daggers who went in front on 16 minutes. Matt Ritchie's corner flew over everyone except Arber at the back post, and the defender took his time before firing in off the crossbar.
From then the Daggers went from strength to strength.
Strevens doubled the lead on 35 minutes, firing in from close range after keeper Peter Barnes had spilled Ritchie's low cross while under pressure from Benson.
Grimsby came out with more purpose after the break. The visitors' best chance to get back into the game went begging on 55 minutes when, just two yards out and with the goal at his mercy, Peter Bore skewed his effort from James Hunt's cross-shot.
And just seven minutes later it was all over for Mike Newell's men when Benson, on his return from injury, scored the goal of the game. The striker chested down Strevens' perfect cross before slamming the ball into the top corner.
Strevens put the icing on the cake with a well-taken header from Jon Nurse' cross in the final minute.
It was an impressive performance by the Daggers but for the Mariners it is now 16 games without a win.