Darlington, who looked to be coasting after scoring a goal in either half, quickly threw the game away.
The home side, already through to the end of season play-offs, took the lead in the 20th minute when midfielder Ricky Ravenhill headed in from close range and, despite a despairing dive from keeper Tony Roberts, the ball rolled over the goal-line.
The visitors missed a great opportunity to equalise seconds before the interval when Sam Saunders headed a Glen Southam cross over the bar from close range.
The home side increased their lead in the 52nd minute when substitute Shaun Reay raced into the area and lobbed the ball over Roberts despite the attention of two Dagenham defenders.
The visitors looked to be dead and buried and they needed to get back into the game as soon as possible.
In the 63rd minute substitute Sam Sloma fired in a close-range shot at the far post and suddenly Darlington were rocking.
A minute later Ben Strevens was brought down inside the area by Ben Parker and the Darlington defender was shown a straight red card and from the spot-kick Dagenham captain Dave Rainford fired in the equaliser.
Suddenly Dagenham smelt victory and the three points that could be enough to secure their league place if fellow strugglers Mansfield lost at home.
Darlington defender Alan White cleared a shot from Saunders off the line as the visitors poured forward.
In the 74th minute the visitors grabbed the winner through Paul Benson who fired in at the far post and from a narrow angle after being left unmarked by the overstretched Darlington defence.