"Try to match him," Bedard said of pitching against Sale. "That didn't work, but I wasn't far off. You just do what you can. Obviously, he was pretty darn good, but we got the win."
The Astros won back-to-back games for the first time since finishing a six-game winning streak with a four-game sweep of the Angels nearly two weeks ago.
Houston did its damage in the fifth, flipping a one-run deficit into a one-run advantage with two unearned runs.
Ronny Cedeno led off, reaching base on an error by shortstop Alexei Ramirez before Sale retired the next two batters. Seemingly out of harm's way, Sale then walked Trevor Crowe and induced a Brandon Barnes grounder.
But Ramirez made an errant throw to second, and Cedeno scored while Crowe advanced to third. Jose Altuve then legged out a high throw on an infield single, plating a fist-pumping Crowe to take the lead for good.
"That there is what you call just straight effort baseball," said Houston manager Bo Porter. "Guys laying out on infield hits, giving it everything they have and hustling on the bases. It's an all-around tremendous effort to get that against one of the more dominant pitchers in our league."
The Astros bullpen combined for three scoreless innings, as Jose Cisnero extended a scoreless-inning streak to 17 1/3 innings and Travis Blackley coaxed a double play to get out of the eighth inning.
Closer Jose Veras earned his 12th save, navigating a tense ninth inning with a popup and a strikeout to strand a White Sox runner.
Altuve led what little offense the Astros could muster, nabbing two hits and an RBI.
Sale was otherwise brilliant, fooling Houston hitters by pounding the strike zone and dropping breaking balls below their eager bats all night. He tossed 124 pitches, including 85 for strikes.
"He's absolutely one of the best pitchers we've faced this year, and if we face him again, he'll be one of the best then, too," Altuve said. "We were doing the best we can, getting runs without hitting it out of the infield. But he had his stuff all night."
Sale's 14 strikeouts marked the second most in his career, second only to the 15 Rays batters he fanned on May 28 of last year.
"It's a tough one as far as the way [Sale] pitched and you want to get better," said White Sox manager Robin Ventura. "You want more out of it than that."
Despite walking three and tossing nearly 60 pitches in the first three innings, Bedard never backed down from his dominant counterpart while hurling a season-high 104 pitches.
He escaped a bases-loaded jam in the second inning, stranded two more in the fifth and left the contest with an improbable lead in a game that featured no earned runs.
"I had a couple innings with a lot of pitches early, but I got stronger and was throwing a lot more strikes later to get the quick outs," Bedard said.
The veteran lefty has surrendered two runs or fewer in six of his last seven starts, becoming a key cog in a burgeoning Houston rotation.
It's the kind of rotation that's becoming more capable of beating an ace no matter the Houston starter, and the Astros proved it for one of their more rambunctious home crowds of the season on Friday night.
"This game speaks to the resilience these guys have played with all year," Porter said. "We created some opportunities in the fifth that might not have been there otherwise with our aggresiveness. That's a pretty impressive arm over there. [Sale'sall as advertised."
"At the same time, I think we manufactured what we needed to and matched their guy. I can never complain about the effort, and tonight we got the result."