An own-goal from Dagenham midfielder Abu Ogogo handed Chesterfield a 1-0 win - their first away victory of 2013.
Wayne Burnett's first home game in charge of Dagenham ended in disappointment and his side have now won just once in their last eight games.
It was against the run of play when Chesterfield went in front after 19 minutes.
James O'Shea whipped in a low cross and Ogogo could only steer an attempted clearance into his own net.
Earlier, Spireites goalkeeper Tommy Lee saved well from Luke Wilkinson, while Daggers striker Sam Williams planted a header wide.
Matt Saunders also went close for Dagenham when he clipped a 20-yard free-kick just over the crossbar.
Luke Howell crashed a low drive narrowly wide early in the second period, before Chesterfield youngster Armand Gnanduillet glanced a header off target from close range.
The Daggers almost levelled spectacularly when Ben Strevens' superb overhead kick was brilliantly saved by Lee.
Chesterfield were rescued by the woodwork in stoppage time as Wilkinson's close-range effort struck the crossbar.