The win sees Houston jump ahead of the Columbus Crew and Philadelphia Union in the East to avoid playing a tricky wild card play-in game midweek.
Instead, the Dynamo will have home field advantage against the third-place Union in a two-game aggregate series following the wild card matches.
Adam Moffat opened the scoring in the first half with a spectacular strike from distance, while Bobby Boswell and Carlo Costly added goals in the second half to ensure all three points for the Dynamo. Jack McBean scored a late goal for Los Angeles, the first of his career.
Moffat provided one of the more stunning strikes of the season in the 27th minute, collecting a loose ball and hitting a rocket from distance to find the upper corner.
Houston then doubled the lead in the 48th minute through Boswell, who fired a quick shot into the side-netting after a failed clearance from the Galaxy defense.
Costly added a third for Houston, heading home a cross at the back post in the 74th minute for his first of the season.
The only sour note on the night came in the 89th minute, as McBean took a pass from Chad Barrett and slotted a shot into the back of the net to spoil Tally Hall's clean sheet.
Los Angeles, with the Supporters' Shield already under its belt, had nothing at stake in the match, and took the opportunity to rest some of its key players. Regular lineup fixtures Landon Donovan, Robbie Keane, David Beckham, Todd Dunivant, and Omar Gonzalez were all not in uniform for the contest.
Houston (12-9-13) finishes the campaign with a six-game unbeaten streak in regular season play, enough to improve to 49 points on the year. Los Angeles (19-5-10) finishes with a league-best 67 points to guarantee home field advantage throughout the postseason.