Houston exploded to four second-half goals in running past Chivas USA.
Barnes got his first with a powerful header in the 39th minute from a corner, putting Houston up at the break.
Eric Avila pulled Chivas level just after the break when he headed home a rebound from a Carlos Alvarez shot that came back off the post.
Barnes had Houston back in front three minutes later, slipping in behind the Chivas back four and slotting home to give his team a 2-1 lead.
Will Bruin added a goal after slipping through in the 63rd - his seventh of the season - to make it 3-1.
Then, Oscar Boniek García tacked on two late goals to run the scoreline up to 5-1. Garcia got his first of the season off a pass from Bruin in the 79th and his second from the penalty spot in stoppage time.
The win moves Houston to 43 points, three clear of the fifth placed New England Revolution.