A late goal from substitute James Hanson rescued a deserved point for The Bantams in their first game since their Capital One Cup Final defeat to Swansea City.
Despite largely having the upper hand in terms of possession and chances, City fell behind to Luke Howell's precise finish with just over 20 minutes remaining but Hanson's 9th goal of the season spared The Bantams' blushes.
It didn't take long for the visitors to show attacking intent and after Matthew Saunders' cross was cushioned neatly by Sam Williams it was Ben Strevens who proceeded to blaze a half volley over the bar from the edge of the area.
The game was starting positively and Rory McArdle missed a glorious opportunity of firing City ahead in the early stages. Kyel Reid's freekick was cleared as far as Michael Nelson who looped the ball back into the area, McArdle beat the offside trap to steal in at the far post but he got under the ball and fired well over on the volley.
Daggers' winger Medy Elito forced Jon McLaughlin into a smart save shortly after when he beat Michael Nelson with trickery before rifling a powerful shot that McLaughlin managed to tip behind for a corner kick via the crossbar.
The game was looking set to be a scrappy affair but The Bantams gathered momentum leading up to the half time interval. Andy Gray came close to opening the scoring when Nelson's flick on dropped into his path, but his goal bound shot was blocked away for a corner.
Rory McArdle then came close when he met Kyel Reid's corner with a header that looped up and dropped narrowly wide of Chris Lewington's far post.
City skipper Gary Jones then tried getting in on the act when Stephen Darby found him in space with a pass infield, he surged forward but his low drive failed to trouble Lewington and bobbled harmlessly on, a couple of yards wide of the target.
Early on in the second half, Dagenham & Redbridge were awarded a dubious penalty kick by referee Chris Sarginson. The visitors had a man over on the edge of the area and Luke Wilkinson received the ball and charged into the area, Kyel Reid came across him in an attempt to defend the situation and Wilkinson went down in a heap after he had perhaps had his heels clipped by The Bantams' winger.
Sam Williams stepped up to take the spot kick but he fired his attempt wide of Jon McLaughlin's right hand corner to let City off the hook.
Rory McArdle and Michael Nelson were proving to be a constant aerial threat in the visitors' 18 yard box and it was the latter who forced Lewington into action. Gary Jones' teasing delivery towards the far post was met by the head of the former Kilmarnock centre half but Lewington managed to claw the ball away from inside the goalmouth.
City were reacting well to the second ball and this time it was Garry Thompson who looped the ball hopefully back into the area; the ball dropped to Andy Gray at the post and he did excellently to juggle the ball away from a couple of defenders but he hammered his shot wide of the target.
The Daggers' front two pairing of Ben Strevens and Sam Williams looked lively for large parts of the game and it was Williams on this occasion who came close to scoring. Oluwafemi Ilesanmi's incisive pass found the feet of Williams inside the area and he twisted and turned before curling a shot with intent that flew inches wide of the far post with Jon McLaughlin scrambling to get there.
Kyel Reid's short corner allowed Gary Jones to fizz a cross into the area and the ball dropped kindly to Rory McArdle who showed predatory instinct to turn and fire a dangerous shot towards goal that took a slight deflection and went behind for a corner kick.
Approaching the 70th minute, the visitors went ahead. After City failed to clear their lines, Ben Strevens pounced to race into the area; his low cross was neatly flicked into the path of Luke Howell by Sam Williams and Howell dispatched a first time shot expertly into the bottom corner from just inside the area.
Alan Connell was introduced from the bench late on and he almost grabbed an equaliser; he found a yard inside the area to hit a dipping shot towards goal that dropped narrowly over the bar.
Phil Parkinson's men were pressing hard for the equaliser and they snatched it late on. The impressive Zavon Hines produced an in-swinging low cross that was helped on by Nahki Wells before James Hanson popped up at the far post, beating the offside trap to tap in from close range.
The Bantams didn't stop there and almost grabbed a winner in the first minute of injury time through Nahki Wells; Gary Jones' freekick was knocked down effectively by James Hanson and the ball ran through to Wells at the far post who sneaked a shot past Chris Lewington from a tight angle, but Daggers' skipper Abu Ogogo was on hand to hack the ball clear from under the crossbar.
Phil Parkinson's men had got off to a somewhat mediocre start to their 'new 15 game season' and despite edging the encounter they could only manage a point. The result adds extra spice and meaning to Saturday's Yorkshire derby against York City and should The Bantams come away from Bootham Crescent with all three points then there is surely grounds for a late play-off surge to begin.