Chris Birchall took a shot for the Galaxy and it appeared to be heading well wide of the net when Houston's Lovel Palmer touched it with a hand.
That brought a penalty call from referee Chris Penso and Donovan scored for the eighth time this season.
Los Angeles (7-2-5) is unbeaten in its last three games and maintained a five-point lead over Dallas at the top of the Western Conference. Dallas, which recorded a 1-0 decision over Seattle Wednesday, has played two fewer games than Los Angeles.
Houston (3-4-5) is winless in its last five.