Eric Alexander gave New York a 1-0 lead at the 14-minute mark, and the Dynamo tied it 4 minutes later on a Jason Johnson tally.
But New York (13-9-6) went ahead to stay in the second half on Henry's goal, followed by insurance tallies from Johnny Steele and Lloyd Sam.
With the win, New York pulled even with Sporting Kansas City atop the Eastern Conference with 45 points.
Houston (10-10-7) remains out of the playoff picture in sixth place in the East.
Notable deaths of 2014 [PHOTOS]