The hosts got off to a dream start when they took the lead through a David Horst header after only a minute of play.
But Giovani equalized three minutes later after taking advantage of a Houston defensive slip-up at the edge of the penalty area to fire home his first goal of the season.
Baggio Husidic then gave the Galaxy the lead on 21 minutes before captain Steven Gerrard picked out Giovani around the penalty to box. The Mexican gathered the ball and sent the his effort beyond Joe Willis for his second goal of the evening.
Gyasi Zardes put the game beyond doubt early in the second half when he tapped home from a Sebastian Lletget pass.
Gio's fellow Mexican forward Erick "Cubo" Torres played the last 33 minutes of the game for the Houston Dynamo.
The Galaxy next play host to Real Salt Lake at StubHub Center next Saturday.
You can watch Giovani dos Santos brace below: