Bruin's tally in the 17th minute on a converted a pass from Boniek García put the Dynamo (3-1-0) ahead to stay and Barnes doubled the advantage with a 42nd-minute header.
The victory tied the MLS mark for most home games without a loss in all competitions. Houston will attempt to break the league record in an April 13 home contest against Chicago.
A stoppage-time header from Chris Wondolowski banged off the post for the Earthquakes (2-2-1).
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