Evan Gattis' homer closed the deficit to 3-2, Chris Carter's three-run homer in the sixth gave the Astros a two-run lead, and Marwin Gonzalez added a homer later that inning that proved to be the difference.
"I can't say enough positive things about what Feldman did mentally and physically tonight," Hinch said. "To have a first inning like that, control the damage the best he could. He had some good approaches against them.
"To have a three-run first inning, it's easy to shut it down and consider it a bad game. All he did was the opposite."
Feldman (3-4) recovered, striking out a season-high 10 batters and snapping a two-game losing streak.
"It was a rough first inning," Feldman said. "Moving forward, I can just get the guys out in the first inning like I'm trying to. I dug us in a little bit of a hole. But guys swung the bat great and the defense was good.
"I just tried to limit the damage. It was all lumped all together at once in the first inning."
After getting the game's leadoff hitter Devon Travis to strike out, the next four Blue Jays reached base. Josh Donaldson, who has reached base safely in 34 games against Houston, doubled. Jose Bautista then walked and Russell Martin followed with a two-run triple. Justin Smoak, who has been a nemesis throughout Feldman's career, scored Martin on a single, putting the Blue Jays up, 3-0.
But then Feldman settled down and got a better feel of his breaking ball as the game went on.
"The first inning was a little rough but after that I felt fine," Feldman said. "We got some big hits and got everybody fired up."
Feldman allowed five hits with three walks. He retired the Blue Jays in order in the third, fourth and sixth innings before leaving with two outs in the seventh and the Astros ahead, 6-3.
"He continued to put zeroes up," Hinch said. "I wanted him to finish the seventh inning until a guy got on base. After the first inning, to be able to hand the ball over to the bullpen in the seventh inning is pretty remarkable."
Richard Dean is a contributor to MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.