Strevens scored two goals and set up a third to leave the Daggers sitting on top of League Two having netted nine goals in winning their opening two fixtures.
Lincoln were disrupted when midfield playmaker Stefan Oakes had to pull out ten minutes before kick-off after suffering a leg injury in the warm-up.
But they started well and went in front only to fall away badly in the second half.
Lincoln took the lead in the 18th minute with their first real attack of the game.
Skipper Scott Kerr chipped the ball into the box for Lenell John-Lewis to rifle home a first-time shot.
City kept up the pressure and a long ball over the top released Kevin Gall.
The striker forced his way past Dagenham keeper Tony Roberts but went too wide and failed to find the net with his shot.
Then Dany N'Guessan was narrowly wide with a left-foot shot in the 38th minute.
The second half was a different story with Dagenham taking control.
Lincoln's game became riddled with errors and it was no surprise when Dagenham levelled things up in the 66th minute.
Sam Saunders fired in a cross from the right which Lincoln keeper Rob Burch could only push out.
The ball fell to Strevens who had plenty of time to place his shot into the empty net.
Another defensive mistake by Lincoln let in Solomon Taiwo, whose shot from 25 yards was narrowly over the top.
Lincoln's defensive performance disintegrated into a shambles in the 76th minute when a mistake by Janos Kovacs put Burch in trouble.
The keeper blasted his clearance against Paul Benson. The striker was first to react to the loose ball but from a narrow angle fired his shot against the post and watched helplessly as the ball rolled across the face of the goal to safety.
Dagenham went in front in the 79th minute when Saunders put the ball into the box and Strevens got in front of Burch to head home.
Lincoln's misery was completed in the last minute when Burch was left stranded outside his area and Strevens ran on to set up Paul Benson for a tap-in goal.