Craig Robson's own-goal gave the Reds a priceless away win to move them up to third in the Vanarama National League - watch match highlights here.
Dagenham had a goal ruled out for offside before Kevin Lokko was shown a straight red card in the 32nd minute. The Daggers had another disallowed in the 89th minute, and then Wrexham struck.
"I don't think we've had a lot of luck this season to be entirely honest," said Keates. "I think we've had a little bit today. Maybe one or two, definitely one, offside goals have gone in our favour.
"Full credit to the lads. They kept going and kept going. First half we played really well, first 20 minutes I thought we were exceptional.
"The sending off changes games and if you score early your life becomes a lot easier.
"Fair play to Dagenham, they were outstanding when they went down to ten men and as I said we had a bit of luck."
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