With just seconds remaining, the midfielder cut in from the right and fired a rasping left-footed drive past Tony Roberts into the bottom corner.
Defeat was harsh on Daggers as they dominated large parts of the first half.
Danny Foster had a goal disallowed while Doug Loft's spectacular drive was superbly turned over the bar by Shwan Jalal.
After the break, the Cherries improved and Jeff Goulding hit the post before shooting wide of an open goal from a tight angle.
However, Goulding's miss mattered not as Molelsey snatched victory right at the death.