The Daggers blew away the Blues in front of the BT Sport cameras, scoring four goals in the second period - watch match highlights here.
Michael Cheek's late brace wrapped things up after Sam Ling and Luke Howell put John Still's side ahead.
Their goals have moved Dagenham up to fourth, having won their last three games.
"We were close last season," Still told BT Sport. "I think we've played well this year, we've always been in and around it.
"We were outstanding in the second half against Chester, in particular up front.
"We've overcome some injuries and we've played, by and large, ok all season. I always say, in the second half of the season, the so-called 'best teams' will start to put it together."
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