Scherzer (3-1) threw six scoreless innings while winning his third straight start, allowing four hits and striking out seven. Scherzer became the first pitcher in team history with at least seven strikeouts in each of his first six starts.
Scherzer's strong outing helped the Tigers win for the fourth time in five games, and shut down the powerful White Sox offense for the second straight day.
Chicago had a chance to score in the third. Eaton walked with one out, advanced to second on Gordon Beckham's single and reached third on a Jose Abreu fielder's choice but was stranded when Adam Dunn struck out.
"He's great, he's always tough," Ventura said of Scherzer. "You get some guys on, you get opportunities and that's when good pitchers really show their stuff. He did that today. We at least got him a high pitch count and he couldn't get eight or nine innings. But, he's just tough."
On Tuesday, Justin Verlander and two relievers held the White Sox to seven hits in a 4-3 Detroit win. Scherzer and the Tigers continued that Wednesday against a team that started the day first in the American League in runs and second in home runs and slugging.
"There's 29 other managers that would like to be able to do that," Detroit's Brad Ausmus said of starting Verlander and Scherzer on consecutive days.
Detroit was one out away from its first shutout of the season, but Tyler Flowers' single off Evan Reed gave Chicago its run.
Alexei Ramirez went 1 for 4 to reach 40 hits, breaking Paul Konerko's White Sox franchise record of 39 hits through April, set in 2002.
"(Konerko) congratulated me in front of the dugout so I kind of lifted my helmet up and said 'Thanks,'" Ramirez said through an interpreter.