Dagenham and Redbridge midfielder Abu Ogogo's own goal handed Chesterfield their first away victory of 2013.
It was against the run of play when, on 19 minutes, James O'Shea whipped in a low cross and Ogogo could only steer an attempted clearance into his own net.
Following John Still's midweek exit for Luton, it meant interim manager Wayne Burnett's first home game in charge of Dagenham ended in disappointment.
But Chesterfield were rescued in injury time when Luke Wilkinson hit the bar.
The Daggers have won just once in eight games to slip to 15th in League Two, only six points clear of safety, a place behind Chesterfield, who are five points better off.
VIEW FROM THE DRESSING ROOM
Chesterfield manager Paul Cook told BBC Radio Sheffield:
"Football's about winning at the end of the day and we've won today.
"We had a lot of players back, which is pleasing, so coming down here I was very confident we could get a clean sheet.
"Whether we could score was always going to be an issue, because we haven't been scoring.
"We've not created loads of chances, but we've won and that's the pleasing thing for this club."