The Minnesota Twins’ Max Kepler hits a two-run home run off Chicago White Sox pitcher Reynaldo Lopez in the third inning Tuesday in Minneapolis. (AP photo)

MINNEAPOLIS — The Minnesota Twins have been in first place in the AL Central for all but 13 days this season, a perch the Chicago White Sox have been aiming for during this extended rebuilding project.

If they can make that big jump in 2020, Lucas Giolito will surely be a major factor.

Giolito pitched a three-hit shutout of the second-highest scoring team in the major leagues, racking up 12 strikeouts for the White Sox on Wednesday in a 4-0 victory for their first series win over the Twins in two years.

“He’s a tough customer, and he was on his game,” Twins manager Rocco Baldelli said. “He pounded the strike zone, but he also has elite stuff, too.”

Giolito (14-6) allowed only one runner past first base, a double by Jonathan Schoop in the eighth. The 25-year-old fanned Jake Cave to finish that inning and reach double-digit strikeouts for the third straight time, the first White Sox starter to do so since Chris Sale did so in eight consecutive turns in 2015. The last right-hander with a streak that long for the team was Edwin Jackson, with three in a row in 2010.

Giolito also matched Cleveland’s Shane Bieber for the major league lead with his third complete game this season, though one was a five-inning, rain-shortened contest against Toronto before he blanked Houston with a four-hit shutout on May 23. Giolito got there this time with a career-high 115 pitches, without a walk.

“If you asked me last year, say you’d throw two complete-game shutouts next season, I don’t know if I would have believed it,” Giolito said, “but it’s the work I put in in the offseason, coming in pitching with confidence every single time.”

The Twins beat the White Sox 10-3 on July 25, and Giolito gave up seven hits, seven runs and four homers in five innings in that game. Since then, he’s 3-1 with a 2.12 ERA and 53 strikeouts in 34 innings. He said a recent change to his between-starts weight room routine has helped him increase his late-game velocity.

One of the myriad prospects collected by the White Sox during their systematic dump of high-priced veterans, Giolito was one of three players acquired from Washington for outfielder Adam Eaton prior to the 2017 season.

“It was able to allow us replenish our system,” manager Rick Renteria said.