NEW YORK -- The Yankees waxed the White Sox 6-1 on Saturday to earn their sixth straight win behind two players.

One, Juan Soto, was expected to lead the club to victories after he was acquired in December. He smashed two home runs, both long beyond Yankee Stadium's short porch in right field, to emphatically snap out of a mini personal skid with his first multi-home run game as a Yankee.

The other, Luis Gil, was expected to begin the season in the minors, honing his craft, waiting for an opportunity. Instead, Gil continued his unforeseen breakout campaign Saturday, delivering the best start of his young career with 14 strikeouts -- a Yankees rookie record -- on 98 pitches over six innings as New York improved to an AL-best 32-15.

The 25-year-old right-hander recovered from a 29-pitch first inning to produce 27 swing-and-misses behind a fastball that touched 100 mph and a changeup he has developed into a devastating offering. At one point, he struck out nine of 10 hitters. He held the White Sox to five hits and one walk. In the end, he lowered his team-best ERA to 2.39 across nine starts.

"Today felt like, maybe, his best one," Yankees manager Aaron Boone said.

Gil is in the rotation only because Gerrit Cole isn't. Cole began the season on the 60-day injured list after being shut down in mid-March with an elbow injury. On Saturday, the team's ace took a significant step forward in his rehab -- logging a 40-pitch bullpen session, divided in two to better simulate a game experience. He remains encouraged in his return to the mound.

For now, Cole is playing the part of assistant pitching coach -- and making an impact on his replacement. Gil credited an increased focus and Cole's tutelage -- during games and in between starts -- for his success after his performance Saturday.

"I have a teacher, Gerrit Cole, who's teaching me how to pitch, how to handle situations and how to execute," Gil said in Spanish. "And that's what we're doing, what he teaches me, and we're applying it in the game."

Gil has been dominant in May after posting a 4.01 ERA in five April starts. Since then, he has allowed just two earned runs with 27 strikeouts in 24 innings across five outings. He made history Saturday by breaking Orlando Hernández's Yankees rookie record for strikeouts in a game. Hernández, who set the mark in 1998 with 13 strikeouts, happened to be in attendance Saturday to throw out the first pitch.

"It was a pleasure to meet him," Gil said. "He was a great pitcher. I loved getting to meet him."

Chicago's only run off Gil came on Andrew Benintendi's two-out, check-swing RBI double to open the scoring in the first inning. The lead was fleeting. Soto responded in the bottom of the frame, smashing a pitch from Brad Keller 112.5 mph for a solo home run. He did it again in the fifth inning, this time launching a pitch from Keller 437 feet to right field for his 11th home run of the season. He finished the day 4-for-4 with a walk and three RBIs.

Soto's explosion came after he went 4-for-31 (.129) without a home run over his previous eight games. The relative struggles were enough for him to take additional batting practice several hours before the Yankees and White Sox opened their series Friday. Soto took swings with hitting coach James Rowson and assistant hitting coach Pat Roessler. He then went 1-for-4 with a double, hitting the ball hard in play three times, in a Yankees win.

"Last night," Boone said, "was the prelude to today."

Soto declined to share what he worked on specifically during Friday's extra hitting session, but he noted he was searching for the "feeling" he had over the first five weeks of the season when he was dominating pitchers on a daily basis.

Did he get it back?

"I think so," Soto said with a smile.