Henry broke a scoreless tie in the 29th minute when he fired a right-footed shot into the bottom right corner of the net, beating a diving save attempt by D.C. goalkeeper Bill Hamid.
Olave doubled the advantage in the 36th when he redirected a Brandon Barklage header for his third tally of the season.
New York (2-3-2) won for the second time in three games.
United (1-4-1), meanwhile, dropped a third straight.
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