The win enabled the Astros to avoid a three-game sweep in the interleague series against their state rivals, as Houston took advantage of a poor showing from the Rangers bullpen after starter Colby Lewis had pitched brilliantly.
The right-hander was in fine form, allowing just three hits through seven scoreless innings but his good work was undone by reliever Dave Bush and closer Neftali Feliz, who gave up five runs between them over the last two frames.
"I'm sure his (Feliz) arm wasn't as live as it would have been on a fresh night because he threw 40 pitches last night," Downs told reporters.
A passed ball allowed Johnson to score and tie the game before Downs, pinch hitting for Clint Barmes, completed the comeback with his fifth home run of the season.
"We had the right guy in the right spot," Rangers manager Ron Washington said. "We're not going to make any excuses. We didn't get it done."
Texas scored a run in the first inning and Nelson Cruz extended the lead to 2-0 with a solo blast in the fifth inning.
(Reporting by Mike Mouat in Windsor, Ontario. Editing by John O'Brien)