Trailing 2-1 entering the frame, the Astros scored twice to grab the lead -- all with two outs.
After Rex Brothers (0-1) recorded two outs for Colorado, Jose Altuve and J.D. Martinez collected singles. Carlos Lee then grounded to third, but the Rockies' Jordan Pacheco threw it away, allowing Altuve to score the equalizer.
Bogusevic then proceeded drove in Martinez with a single to right, and the Astros held on to take the rubber match of their season-opening three-game series.
Brett Myers registered his first save despite a shaky ninth inning and Wilton Lopez (1-0) earned the victory after getting the final two outs in the eighth.
Rockies starter Juan Nicasio tossed seven innings of one-run ball, yielding five hits and a single walk while fanning four.
Wilin Rosario socked a two-run homer for Colorado.