Hill scored on a long blast in the 9th minute and Akpan doubled the advantage in the 77th on a header as the Rapids (11-19-5) closed out their season with two straight wins.
The Dynamo, meanwhile, ended at 14-9-12 (53 points).
They had earlier clinched the fifth and final seed in the Eastern Conference and Coach Dominic Kinnear fielded a squad of mostly backups.
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