Ching collected a short cross from Colin Clark in the area, rising to head the ball from 10 yards inside the right post, leaving United goalie Bill Hamid no chance.
Ching also played a part in the Dynamo's first goal when he won a penalty in the first half and Brad Davis converted on the kick, his first goal of the year for Houston (4-6-7).
United (4-5-6) took a lead in the 73rd minute when Andy Najar lost the ball deep in the area, but Charlie Davies got control and hammered it into the net from 6 yards out.
Chris Pontius also scored as United failed to win at home for the sixth time in eight matches.
Notable deaths of 2014 [PHOTOS]