The Daggers' win piles the pressure on Bury boss Chris Casper, and helps their own cause - league survival and movement up the table and away from the drop zone. This victory was their first in four outings.
The 27 year-old Strevens struck in the 21st minute and the 62nd minute, converting crosses from the lively right winger Sam Saunders.
His opener was a header from six yards - and he was almost gifted the freedom of Bury by the home defence.
And then Strevens was on hand to take advantage of a real goalkeeping howler from Jim Provett, who dropped an easy Saunders cross.
While the visitors are still rooted deep in relegation trouble, the Shakers have dropped like a stone after being in play-off contention earlier in the season.
The Bury fans were obviously furious with this display, chanting 'Casper Out' for the latter part of the second half.
Andy Bishop had the home side's best chance to get back into the game at the end of the first half - but lifted a through ball wide of the woodwork.
Daggers' striker Jon Nurse then had what would have been a second goal ruled out for off-side just a couple of minutes after the break.
Strevens will take all the plaudits for his goal haul - but Saunders was superb with his wing play and delivery. He continually tested the Shakers defence and had two efforts of his own in the first eight minutes of this contest.