Dagenham will feel hard done by after having a goal ruled out which appeared to have crossed the line in the first half and controlling much of the second.
Stockport took the lead after four minutes when Leon McSweeney finished a lovely move with a right-foot cracker which left Daggers keeper Tony Roberts with no chance.
Manager John Still responded by switching Dagenham to a 4-4-2 formation and brought on Ryan Hall for his debut after arriving on loan from Crystal Palace.
The tactical change almost paid off immediately when Hall's left-footed corner was headed onto the underside of the bar by Ben Strevens on 25 minutes.
The balled appeared to bounce over the line before being hooked to safety, but thankfully for the travelling Stockport fans, the referee waved away the home side's protests.
Stockport continued to have the better of the play and went close to doubling their lead when Anthony Pilkington was put through on goal after half an hour but he dragged a tame shot wide.
Pilkington tried his luck for Stockport with a left-foot drive from the edge of the area after 77 minutes but it was a rare chance in a game that lacked any shape after the break.
Hall had the best chance of the match for Dagenham when he was played through on goal after Shabazz Baidoo brought down Jon Nurse's right-wing cross, but the ex-Crystal Palace player inexplicably missed from five yards.
Nurse was supplier again five minutes from time but Strevens could only volley over after receiving the right wing cross at full-stretch.
Glen Southam went close with a rasping right-foot drive from 20 yards that shaved the top of Stockport's post, but it was all in vain as Stockport ran out fortunate winners.