If the 23-year-old left-hander earns his ninth victory in his 28th and final start of 2016, it would match the win total from his rookie season.
It would also complete a successful late-summer rebound from the 2-8 record he owned on July 31 after giving up five runs on eight hits in a 6 1/3-inning outing during Chicago's 6-4 loss to the Twins.
Entering Friday, Rodon is 8-10 with a 4.08 ERA. He went 3-0 with a 1.47 ERA in five August starts, and he is 3-2 with a 4.80 ERA over five starts in September. The White Sox (77-82) have won seven of his past 10 starts.
In his most recent start, Rodon delayed the Cleveland Indians' American League Central clincher with a superlative outing Sunday. He threw eight scoreless innings and struck out a career-best 11 in the White Sox's 3-0 victory. He gave up two hits and walked three.
"That was the best I've seen him," White Sox manager Robin Ventura said. "Strike one was the biggest thing, and it was with authority. It was placed well. After that, it just seems like he got better as the game moved along. A couple of guys get on, he seems to turn it up in key situations in the middle of the game, late in the game. He just had it all."
Rodon is 2-2 with a 3.71 ERA in six career games (five starts) against the Twins, including 2-1 with a 4.32 ERA in four starts against them this season.
Minnesota (57-102) snapped a three-game losing streak Thursday with a 7-6 victory over the Kansas City Royals.
The Twins, who come into the series with 10 losses in their last 12 games, will send out right-hander Tyler Duffey (9-11, 6.18 ERA) for the 26th and final start of his second big league season.
Duffey beat the Seattle Mariners on Saturday, allowing two runs on four hits with no walks and four strikeouts over seven innings.
"I finally found a good rhythm to keep me composed, to keep from pulling off the ball," Duffey said after the game. "I located a lot better today. Got behind a couple times, but defense bailed me out, had some good plays in the outfield and scored enough to win."
He is 0-1 with a 4.63 ERA in two career starts against the White Sox. In his lone appearance against them this season, he took the loss on May 8 after allowing three runs in seven innings.
Duffey spent most of the season in the Twins' rotation before being sent down to Triple-A Rochester in late August. He rejoined Minnesota when rosters expanded earlier this month.
Shields has the second-most losses in the American League behind Tampa Bay's Chris Archer, who beat the White Sox on Thursday go close his season at 9-19.
The White Sox have outscored the Twins 88-71 through 16 matchups this year. The teams have split the past 10 games after Chicago won the first six.