The visitors took a 19th-minute lead when Matt Saunders crossed from the right and Sam Williams eluded the attention of Guy Branston to send a sweet right-foot volley past home keeper Sam Walker from 12 yards.
The Daggers had already been indebted to a brilliant triple save by Lewington after 15 minutes as he dived to deny Oliver Norburn and David Clarkson twice.
In the second half, Lewington kept out shots from Tom Eaves and Joe Anyinsah as the Londoners defended for their lives.
Rovers poured forward without creating enough clear chances. The final whistle was greeted with loud jeers from home fans as their team stay in the bottom two places.
For Dagenham & Redbridge, it was the perfect smash-and-grab raid.