The first was hit to deep left-center on a full count that followed a double by Dexter Fowler. The second was hit to the left-field Crawford Boxes, also with Fowler on base, putting the Astros up 8-1.
Since Peacock became a starter on April 20, the offense provided 13 runs of support in his previous five starts.
“Our hitters came out swinging,” Peacock said. “It’s a big confidence builder for them and a big confidence builder for us.”
The Astros have won four of their past five games, while the White Sox have lost six of eight. After taking two of three from the Rangers and White Sox, Houston has won back-to-back series for the first time since last August.
The Astros improved to 12-3 when hitting two or more home runs. They are 1-17 when they fail to hit a homer.
After a Chris Carter homer in the second inning gave the Astros an early lead, Jonathan Villar sparked a rally with a two-RBI single that scored Jesus Guzman and L.J. Hoes. Guzman advanced to second on a throwing error by left fielder Alejandro De Aza then stole third and scored when catcher Adrian Nieto’s attempt to throw him out skipped into the outfield.
The Astros had 10 hits in the game and have had at least nine hits in eight straight games, the club’s longest such streak since 2008.
“They were swinging it good,” White Sox manager Robin Ventura said. “Any time you get the ball up, especially in this ballpark, you’re going to create a lot of problems.”
Villar later left the game in the seventh inning with a right hand injury, but Porter said the injury was not serious.