Callum Harriot struck in the fifth minute of stoppage time to leave Ben Strevens’ men without a win in seven games in the National League.
Frank Vincent was caught off-guard by a superb delivery from Lewis Page after just five minutes, as Daggers made a bright start.
And Charley Kendall sent a shot on the turn just wide on 12 minutes before Josh Rees sent a great chance over the crossbar.
The hosts had penalty claims turned down midway through the first half, before Ryan Hill cut in and saw a shot held by Ryan Whitley.
The York keeper needed some physio treatment after making the save, but was able to produce a stunning stop to deny Hill again on 29 minutes.
Harry Phipps could not get enough contact on a Jake Hessenthaler free-kick to seriously test Whitley just before the break as the scoreline remained blank.
The visitors made a bright start to the second half, with Kendall picking up a yellow card on 56 minutes.
But Daggers made the breakthrough on the hour when a superb move ended with Page cutting the ball back for Hill to smash home.
Vincent had a great chance to double the lead on 64 minutes, but got too much on his effort, and another fine move ended with Kendall sending Josh Hare’s cross over.
Freddie Sears raced through to force a save from Whitley on 69 minutes, with Elliot Justham saving well with his feet to deny Scott Burgess and then also thwarting Lenell John-Lewis on 82 minutes with a superb stop.
But Hill had to make way for Keenan Appiah-Forson after picking up an injury and York drew level five minutes from time through John-Lewis.
And it got worse in the fifth minute of stoppage time as Harriott grabbed a late winner for the visitors.
Dagenham & Redbridge: Justham, Hare, Tavares, Hessenthaler, Vincent, Rees, Hill (Appiah-Forson 82), Page, Phipps, Kendall (Ibie 90), Sears.
Unused subs: Francis-Clarke, Longe-King.
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