Kick-off was put back an hour due to the visitors' late arrival having travelled north by train and being delayed en route.
City boss Billy McEwan was forced to make one change to his line-up with Anthony Lloyd replacing the suspended Nathan Peat in defence. Dagenham were missing David Rainford through suspension with Jake Leberl replacing him in midfield.
The hour delay to kick-off was soon forgotten by the home fans as, on ten minutes. Martyn Woolford put City ahead with a stunning strike. After receiving Craig Farrell's clever pass, the former Frickley man ran across field and unleashed an unstoppable curling right-foot shot from 20 yards inside Tony Roberts' near post.
Dagenham, the Conference's top scorers, hit back with free-kicks from Sam Saunders and Glen Southam. Striker Craig Mackail-Smith, in top-scoring form at present, saw his downward header from eight yards well saved by Tom Evans, but he beat the City keeper on 31 minutes for the equalising goal.
Receiving a throw-in launched into a packed area, the striker turned Jason Goodliffe and fired over Evans into the roof of the net from 12 yards.
At the other end Clayton Donaldson showed great skill on a heavy pitch, sprinting clear from halfway but his shot on goal from an acute angle was blocked at the expense of a corner.
City had good appeals for a penalty waved away when Woolford appeared to be taken out by defender Danny Foster.
The visitors always looked a threat going forward and almost went ahead just before the break. Emmanuel Panther gave the ball away just outside the area and Saunders found Paul Benson whose shot down to the bottom corner brought a fine diving save from Evans.
City were back in front two minutes after the re-start. Farrell's corner was headed out to the edge of the area where Steve Bowey smacked the ball through a crowd of players. His shot was blocked by an outstretched defender's leg but fell invitingly for Donaldson to stab home his 13th of the season from close range.
A minute later Farrell released Donaldson on halfway and the striker checked back and tried an audacious chip from 30 yards out which only just cleared the bar.
Dagenham were back on level terms on 64 minutes from a well-worked corner routine. The ball was laid back to Southam who had space to strike a powerful drive from 25 yards beyond Evans into the far corner.
Both sides went all out for the winner and City had a chance when Donaldson escaped down the left, ignored Woolford but picked out Neal Bishop's run to the far post and his flying volley flashed across goal.
At the other end Saunders saw his dipping drive beat Evans but his effort flashed just over.
Dagenham's efforts were rewarded with a trademark counter-attack on 77 minutes. Farrell gave the ball away in the visitors half and Benson's long ball over the top set Mackail-Smith free and he coolly slotted past Evans for his second goal of the match.
Woolford could have notched his second of the game when he broke down the middle but his 20-yard effort flashed inches wide. Then, in stoppage time, his close-range effort brought a fine smothering save from keeper Roberts.