It was the second assist of the match for Davis, who leads MLS in the category with eight.
The Dynamo (3-4-6) managed to avoid a second consecutive loss despite playing the final 18 minutes down a man after defender Kofi Sarkodie was ejected for picking up his second yellow card of the match.
Dallas (6-3-4) extended its unbeaten streak to eight games. The Dynamo, meanwhile, went winless in May for the first time in team history.
Dallas defender Ugo Ihemelu got by the Houston defense and headed in Marvin Chavez's corner kick in the 70th minute to make it 2-1.
Andrew Jacobson opened the scoring for FC Dallas 27 minutes into the match with a 15-yard header off a loose ball that resulted from teammate Fabian Castillo's long-range shot bouncing off the crossbar.
Houston forward Cam Weaver tied it in the 43rd minute, beating Hartman with a well-placed 15-yard shot off a crisp pass from the left by Davis. It was Jacobson's first goal of the season.