Houston had been winless on the road until last Sunday, when it recorded a 1-0 decision over Los Angeles.
The Dynamo began the night tied for the lead in the Eastern Conference and improved to 6-2-2.
Bruin scored in the 16th and 78th minutes and he assisted on goals by Giles Barnes in the 28th and Andrew Driver in the 88th. Tally Hall had to make only one save to record the shutout.
D.C. United's four points are the fewest in MLS and the setback dropped it to 1-7-1.