"Trust me, you'll never hear me complain about six runs in an inning," Danks said after his first win in nearly two months, a 10-5 decision over the Tampa Bay Rays on Sunday.
Brandon Guyer's one-out double in the sixth was Tampa Bay's first hit off Danks.
"He'll take it, I'm sure," manager Robin Ventura said. "All things considered, you'd rather have a six-run inning than take your chances going out there trying to throw a no-hitter."
It wasn't until Avisail Garcia's second home run of the game had sparked a six-run inning for a 10-0 lead that Danks gave up his first hit -- and two runs.
"I've been there before," Danks said. "I can't go out there and walk the leadoff hitter like I did. That kind of set the inning off. It wasn't a terrible pitch to Guyer, I believe, but I kind of dug my own grave on that one."
Winning for the first time in 10 starts, Danks (10-11) gave up two runs on two hits in six innings. Guyer's double came after a walk to Curt Casali and a strikeout.
But the White Sox had built a huge lead by then, and the only challenge Danks had left was the pursuit of a no-hitter.
"Anyone who says they don't know what's going on is lying to you," Danks said. "It's a lot of fun just thinking about what could happen."
Garcia had three of Chicago's 12 hits, including his sixth and seventh home runs of the season, while Semien and Jordan Danks each had two hits.
"I think it was a case of Avisail Garcia, the bat in his hand. That was our problem," Tampa Bay manager Joe Maddon said.
The White Sox followed Garcia's second homer with four more hits, including Alexei Ramirez's two-run double off reliever Alex Colome. Rookie Jose Abreu drove in Ramirez with a single for his 105th RBI.
White Sox: 1B Paul Konerko was out the lineup for the second straight day, but Ventura said it is not related to the broken hand that kept him out two weeks.