CLEVELAND -- Pitcher's wins certainly aren’t the most important statistic to Dylan Cease, who finished second in the 2022 American League Cy Young voting.

So even after picking up his first win since April 10 against the Giants during a 4-2 White Sox victory over the Guardians on Tuesday evening at Progressive Field, it still wasn’t the right-hander’s focus for celebration.

“It’s more about how I’m executing,” Cease said. “If I’m executing well and I’m not winning, I can live with it. If I’m not executing well, it can kind of drive me crazy.

“Definitely the best I’ve felt in quite a while. I feel like I’m getting really close to syncing everything up.”

Could the same be true for the White Sox (20-30), who improved to 6-2 during a stretch of 19 games of which 16 are against the American League Central? Tuesday’s total team effort was not without issue, as center field Luis Robert Jr. left in the ninth inning with right hip soreness, although manager Pedro Grifol mentioned it as a quad. 

Grifol added Robert Jr. was day to day with a day off probably coming in Wednesday afternoon’s series finale, as Robert already was in line for a break. Robert had two hits in the victory, raising his May batting average to .370 (27-for-73). 

“Everything we heard, it’s just day to day,” Grifol said.

Cease struck out three and allowed two runs over six innings but relied on a couple of strong defensive plays and timely hitting during a three-run seventh in support. With runners on first and second and two outs in the fourth, shortstop Tim Anderson was able to make a diving stop of Andrés Giménez’s single up the middle and then easily throw out Josh Bell at the plate, with Bell trying to score from second.

“There was absolutely no panic,” said Grifol of Anderson’s play where Bell was waved home. “He dove for the ball, got up, saw the runner -- which was Bell -- and set his feet and made a perfect throw.”

“Plays like that are what end up winning ballgames,” Cease said. “That was huge.”

Romy González made another game-winning play in the sixth after Cease walked Amed Rosario to open the frame. José Ramírez's hard-hit grounder ricocheted off first baseman Andrew Vaughn, but González trailed the play and flipped to Vaughn, who returned to first to make a bard-handed grab.

The original call stood after manager Terry Francona’s replay challenge. Josh Naylor doubled home the go-ahead run in a 1-1 game, but the Guardians (21-27) were held to one run.

“It was tough to tell but I thought that we had him for sure,” González said. “Anytime a ball is hit to my left or anything, I'm always backing up because plays like that happen -- I don't want to say often, but they do happen.

“I was just in the right place at the right time and [Vaughn] was heads up and got back to that bag and barehanded that ball. That was solid."

González followed with a two-run double in the top of the seventh off Logan Allen, scoring pinch-runner Adam Haseley and Andrew Benintendi, who extended his hitting streak to 10 games with a seventh-inning double. Clint Frazier reached on a seven-pitch walk to set up González.

“As soon as I got to third, I let him know,” said González of Frazier's walk. “When they brought in [Enyel] De Los Santos, I told him that was a huge at-bat. Seeing that many pitches, he kind of wore him out a little bit. That's huge. You're just passing the torch. That's what good teams do."

Good teams also win series, which the White Sox could do on Wednesday.

“We just have to come out tomorrow and put together a good baseball game on all facets,” Grifol said. “We just have to come out and play good baseball. We are pitching well, we are playing pretty good defense and finding ways to step on home plate.”