DETROIT -- Andrew Vaughn slammed, Eloy Jiménez crushed and the White Sox pitching staff pieced together nine innings on a bullpen day during an 11-5 victory over Detroit at Comerica Park on Sunday.

The White Sox improved to 76-71 overall and 12-4 against the Tigers. But with all due respect to Detroit, the more important work begins Tuesday when the American League Central-leading Guardians come to Chicago for the two teams' final three head-to-head contests.

Cleveland either will hold a three- or four-game lead over the White Sox, with a Guardians home contest to be played Monday against the Twins. A sweep for the White Sox would make this division pretty much a dead heat, but also give them a division tiebreaker with a 10-9 season series edge.

Even with all that knowledge in mind postgame Sunday, the White Sox weren’t using the ‘S' word.

“You don’t want to be thinking like go and sweep,” White Sox acting manager Miguel Cairo said. “You concentrate on Tuesday, really play hard, go after it and dig in. You are going to win or you are going to lose. Hopefully it’s going to be on our side.”

“Can't sweep if you lose the first game,” White Sox outfielder AJ Pollock said. “So you've got to win that first game and then yeah, you've got to keep pressing the pedal down."

Pollock launched one of three home runs Sunday, and none of them were of the wall-scraper variety. Pollock’s 421-foot blast tied the game at 2 in the second, but it was Vaughn’s first career grand slam during a five-run fifth that gave the White Sox control.

Jiménez and Gavin Sheets drew two-out walks off Detroit starter Drew Hutchison to force home the go-ahead run, before Vaughn connected on a 418-foot drive off Jason Foley on a 1-2 slider.

“Put the momentum on our side. It was a big at-bat,” said Vaughn, who now has a team-best 17 home runs and 73 RBIs. “Sheets, huge bases-loaded walk before that. I got a pitch to hit and gave us some insurance there.

“I was just trying to get the job done. That was plain and simple. He was throwing some tough pitches and left one out over the middle and [I] put a good swing on it.”

Those two home runs seemed like high popups, distance-wise, compared to Jiménez’s 450-foot blast in the seventh inning off Garrett Hill. It was the longest home run of the season at Comerica Park.

Vince Velasquez allowed two runs over the first four innings, with Tanner Banks pitching the final three to get the victory. Banks had a 3:45 a.m. ET wakeup call to leave Triple-A Charlotte in Norfolk and join the team Sunday in Detroit.

Sunday’s start was supposed to go to Johnny Cueto, but he was scratched again with dizziness due to a sinus issue/flu. So, Velasquez didn’t know for sure until Sunday morning.

“Today was big for us. Every win is precious,” Velasquez said. “This is a good way to take the series from Detroit and go back home and do some damage against Cleveland.

“This road trip itself has been very driven in the right direction and right steps for us to do some damage against Cleveland at home. We’ll see how it turns out.”

Now, the White Sox turn their full attention to Cleveland (79-67), which has a 10-3 record in its last 13 games. Aaron Civale, Triston McKenzie and Shane Bieber are the Guardians’ scheduled starters, representing three of the team’s top four in the rotation, while the White Sox have yet to announce a starter for Tuesday.

They probably wouldn’t need a sweep entering at three games back, although they would lose the crucial tiebreaker. But they are coming into the series on a high note, and as of Sunday, Tuesday is their lone focus.

“They’re playing good baseball. I think we’re playing good baseball right now, too,” Vaughn said. “So, you know, it’s going to be a good battle. Just got to go out there and play our game. Pitch well, hit well, play defense.”

“It seems like we're running down the end of the year,” Pollock said. “But if you look at other sports, 15 games is near a full season for NFL. We're coming down to the end here, but there's plenty of games to make up ground."