It was only the Daggers second away win of the season but it was a reward for a positive second half effort which belied their lowly league position.
Poor finishing cost Carlisle a great chance to take an early lead when first Ben Marshall's close range effort was charged down by keeper Tony Roberts then when the ball ran loose Francois Zoko hooked his shot wildly over the bar from eight yards.
Carlisle continued to have the greater share of possession but Bas Savage was a constant threat for the Daggers and had keeper Adam Collin at full stretch to save a raking drive.
The lively Marshall, Carlisle's on-loan Stoke winger, was denied by the outstretched hand of Roberts when it seemed he was about to break the deadlock.
Carlisle could not afford to relax as the visitors went all out for the win and were rewarded in the 81st minute when Elito stole in at the near post to slide home Kayleden Brown's cross from close range. And Green fired home a shot from just inside the area with a couple of minutes remaining to seal the points.
Source: PA
Source: PA