Moffat's stunning strike into the upper corner came in the 27th minute, handing the Dynamo a 1-0 lead.
Houston doubled its advantage in the 48th minute when Bobby Boswell notched a goal following a failed Galaxy clearing attempt and Carlo Costly added a third score in the 74th.
The victory allowed the Dynamo (12-9-13) to finish the year with a six-game unbeaten streak and avoid a wild card play-in game.
Landon Donovan, Robbie Keane, David Beckham, Todd Dunivant and Omar Gonzalez didn't suit up for the MLS-best Galaxy, who finished the regular season with a 19-5-10 mark and have home field throughout the playoffs.
Jack McBean scored for Los Angeles.