Davis' third homer of the series and his American League-leading 10th came in the eighth inning off Will Harris. It proved to be the game winner, traveling 373 feet with an exit velocity of 102 mph.
The seven-inning stint was also a career high for Triggs, who did not walk a batter and scattered five hits.
With Triggs out of the ballgame, the Astros capitalized to trim the deficit in the bottom half of the eighth on Jose Altuve's homer to left off reliever Sean Doolittle, which went an estimated 354 feet with a launch angle of 32 degrees.