Kabamba struck his spot-kick brace midway through the second half to bring Dean Brennan's Bees level at 3-3 before Rhys Browne climbed off the bench to inflict only a second home league defeat on the Daggers.
Josh Umerah put Dagenham in front inside 25 seconds, only for Idris Kanu to level three minutes later.
Goals from Romoney Crichlow and Ryan Hill either side of the break put the Daggers in control before title-chasing Barnet battled back.
"The gaffer told us to keep on believing in the process and the plan that he's got," Kabamba said. "We brought into it and this is a big step in the right direction.
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