Houston took the lead again midway through the half as Barnes tapped home after Bruin took Irwin out of the game, before serving up a simple chance the former Derby County winger.
Colorado got back on level terms just before the half-time whistle thanks to Sanchez's fortunate second, the forward's shot deflecting into the net off Raul Rodriguez.
Houston began the second period in similar fashion to the first as another deflection saw Dynamo retake the lead for the third time.
Miranda's shot rebounded kindly into the path of captain Davis who made no mistake from close range.
Luis Solignac went down the other end but saw his shot blocked, before Bruin missed a chance to extend Houston's lead as Irwin saved once more.
The Colorado goal threat again came from Sanchez, who saw another placed effort saved by Deric, before the Dynamo keeper denied the Uruguayan forward once more at the near post to hand his side all three points.
The Rapids remain at the foot of the Western Conference, four points behind Houston in eighth spot. body check tags ::