Houston started the match superbly and opened the scoring in the 17th minute when Will Bruin found Barnes, who scored the first of his goals by curling the ball into the top corner.
Barnes managed to outdo himself just five minutes later, collecting the ball from 30 yards out before unleashing a sublime effort to leave Michael Gspurning watching the net ripple for the second time.
Clint Dempsey, who recently joined Seattle from Tottenham Hotspur, should have pulled a goal back in the 35th minute but his tame effort was easily saved by Tally Hall.
Dynamo remained in full control after the break but the mood soon turned slightly more nervous in the BBVA Compass Stadium when Seattle opened their account for the evening.
However, Houston refused to allow their opponents build momentum following the goal and the hosts put the result beyond doubt with 16 minutes remaining.
Brad Davis rose highest inside the box to knock the ball down to Bruin and the forward made no mistake from 10 yards as he finished calmly to secure a comfortable win for Houston.