Jamie Smith hit the post just after the interval as the visitors put Houston's proud home record under severe pressure.
Brad Davis had a low strike saved as Dynamo responded by attacking in numbers and the hosts were rewarded when they drew level on 66 minutes.
The equaliser finally came when Barnes slammed into the top corner from just inside the penalty area after being offered the chance to shoot under little pressure.
Bruin, Davis and Martin Rivero all had chances in the closing stages but both sides looked destined to finish level.
Houston had one final chance to snatch a winner in seven minutes of stoppage time, but Bruin clipped the bar with his powerful header and Dynamo were forced to settle for a battling point.