The visitors looked low on confidence and pressed the self destruct button at the start of the second half when they conceded two goals in two minutes, with skipper Jake Buxton being sent off for bringing down Daggers striker, Paul Benson, inside the box.
Daggers started brightly, with striker Ben Strevens firing in a bullet header which Mansfield keeper Jason White did well to palm onto the crossbar.
Strevens came close again in the 23rd minute, when he turned Mansfield skipper Jake Buxton on the edge of the box, before seeing his clever 20 yard lob drop inches over the Mansfield crossbar.
Dagenham skipper Jon Boardman should have given his side the lead in the 29th minute when he nodded inches over the bar from close range after latching onto a deep cross from Sam Saunders.
The Stags' best chance of the first half dropped to striker Nathan Arnold in the 31st minute, when he missed the target with a powerful volley after out-muscling Boardman inside the Daggers box.
The home side came flying out of the blocks in the second half, with Benson firing the ball off a post in the 47th minute after connecting with a clever Saunders cross.
The home side were rocking and Strevens finally gave Daggers a deserved lead when he arrowed a 49th minute header over White and into the net from a Saunders corner.
The Stags threw the game away a minute later, when Buxton was sent off for hauling down Benson inside the Mansfield box, with the Daggers striker stepping up to double his side's lead from the penalty spot.
Daggers should have gone three up in the 70th minute when Boardman rose highest to connect with another quality Saunders delivery, only for White to palm his powerful header to safety.
The home side piled on the pressure in search of a third goal, with Strevens seeing his thunderous 20-yard strike tipped over the bar by White in the 84th minute.