The Dynamo (7-8-6) took control in the ninth minute when Will Bruin settled Davis' diagonal cross and smashed home a left-footer. Davis then added a long-range strike from behind the top of the circle in the 27th minute.
Leonel Miranda capped the scoring in the 88th minute, juking two Galaxy defenders and finishing with a chip shot.
The Galaxy (9-7-7) entered the match in second place in the Western Conference, having won four of their last five. But they struggled to match Houston's energy with temperatures in the 90s.
Erick Torres made his Dynamo debut as a substitute in the 69th minute. Torres signed with Houston as a Designated Player on Dec. 23, 2014, after an all-star season for defunct Chivas USA.