CHICAGO -- That next-man-up philosophy adopted by the White Sox has turned into a next-team-down winning level for the American League Central leaders.

During a 3-0 victory Tuesday night at Guaranteed Rate Field over the Rays, who lead the AL East and feature the best record in baseball, second baseman Danny Mendick singled home the first run of the game during a two-run fourth against Shane McClanahan. Mendick replaced Nick Madrigal, who had surgery to repair a right hamstring tear and will be out for the remainder of the 2021 season.

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Mendick’s single scored Andrew Vaughn, but when the ball got by catcher Francisco Mejía, it was Leury García who dashed home after advancing to third all the way from first base. García started at third base in place of Yoán Moncada, who missed his second straight game with a sinus infection and figures to be out again for Wednesday’s series finale, per White Sox manager Tony La Russa.

"Well, you've got to have speed,” said La Russa of the aggressive play by García. “But talk about multi tools, with the switch-hitting and the ability to play all over. He came from first base, he got a great jump and it all developed ahead of him. He was just steps behind the scorer. That's who he is, not just a great talent, he's a very instinctive player as well."

“It’s really no shock,” said White Sox shortstop Tim Anderson, who had three hits to raise his average to .311. “They just step in and continue to play their role and continue to help us win games. That’s what we ask of them. They are doing everything they can to help us get wins.”

Adam Engel increased the lead to 3-0 in the fifth with his third home run since returning from the injured list on June 4 after dealing with a right hamstring strain. Engel is starting regularly in center with Luis Robert out due to a right hip flexor tear. It takes a village to build a champion.

"Every time I take an at-bat, I'm getting a little more and more comfortable there,” Engel said. “Obviously I've been able to put some good at-bats together there recently.

“That also helps speed up the process of confidence and all that, when you're getting some good results. It's been good to get some hits and put the ball in play hard, and confidence builds as I continue to just try and get that timing back. I'm just trying to help the team win any way I can."

All of this offense was more than enough support for Dallas Keuchel, who allowed just four hits over seven scoreless innings and 102 pitches. The southpaw struck out five and walked one as he put together his third straight quality start and sixth of the season while improving to 6-1 and lowering his ERA to 3.78, with three earned runs yielded in his last 19 innings.

“He's very good at moving the ball many different ways, just kind of letting hitters get themselves out,” Rays center fielder Kevin Kiermaier said. “And that was kind of the case tonight. For the most part, bats were quiet, and he threw the ball really well. So tip our cap to him. Sometimes that happens, even to a good team like us."

“Think about the quality of the competition,” La Russa said. “He was Picasso, just painted beautifully and shut that club out [for] seven innings. What a lift, outstanding. They're a very tough ballclub. I think we both play nine hard innings, and it makes for a good competition."

Keuchel's next start will be in Houston on Sunday, marking his first career start against the team he played for over his first seven seasons. It also will be another top-of-the-division challenge for the White Sox (42-25), who have shown their drive and fortitude against the Rays (43-25) even with top players absent.

“Just going out there every day, giving 100 percent and seeing what happens,” Anderson said. “Max out every day and doing what you are capable of and be that man in the middle: never get too high, never get too low and be a good teammate. The wins will come. We just have to keep pushing and keep picking one another up, and we’ll be in a great spot.”

“These games are ones that you can, good or bad, take a lot from and move toward October,” Keuchel said. “It is just June, so you’ve got to kind of pump the brakes on overhyping yourself and just try to get the job done night in and night out.”