PHOENIX, Ariz. -- Lucas Giolito's signature walk around the mound following strikeouts received a workout during a 4-3 White Sox victory over the Brewers on Tuesday afternoon at American Family Fields.

And it was just Game 1 for the right-hander off the mound during Spring Training.

Over the first and second innings, Giolito fanned Omar Narváez, Hunter Renfroe, Keston Hiura and Mike Brousseau consecutively. He topped out at 97 mph, per the stadium scoreboard, but Giolito hit 95 mph on two of those strikeouts.

Giolito added about 20 pounds of mass through a bolstered weightlifting program this offseason. He felt the positive effects against the Brewers.

“I feel stronger. I feel more stable,” Giolito said. “I feel like another thing that I notice is like when I do misfire one, it’s like I can quickly get back to where I need to be. The mechanics are more locked in. I’m not thinking about any of that stuff out there.

“Coming out of the gate here and throwing good sliders, I didn’t like hang any. I didn’t get behind any. That was a huge issue in the first half last year and we almost had to kind of relearn to throw the slider at the midpoint. Now, I feel that pitch is coming out very nice: good velocity and good break on it. And the curveball as well. Threw three curveballs today, two for strikes and one was probably a strike. I feel like the shape and everything is good there as well.”

All four of Giolito’s pitches worked during his three scoreless innings, in which he also yielded one hit and one walk. He noticed the overall uptick in velocity and was right where he wanted to be.

The shortened Spring Training following the lockout has left doubts about pitchers getting stretched out enough innings-wise and pitch count-wise to go above five innings at the outset. But through his offseason preparation and in conjunction with the White Sox, Giolito has no fear in that area.

“No, I’m feeling good. We are on a very nice schedule for that,” Giolito said. “I felt very strong, like I could have gone out for more. We are just going to go step by step and be ready for hopefully six, or whatever, Opening Day.”

Does Giolito’s “Opening Day” reference refer to the season debut for the White Sox on April 8 in Detroit or his first game of the season? Do those two dates happen to be one in the same, meaning Giolito will make his third straight Opening Day start for the White Sox?

Lance Lynn has a case for that honor, finishing third in the 2021 American League Cy Young voting. But with manager Tony La Russa having yet to make that start official, Giolito remained non-committal on Tuesday.

“Well, considering how Lance pitched last year, I think he’s more than deserving,” Giolito said. “But I don’t think it’s been announced yet, so I’m totally cool with whatever as long as I get the ball, and get to go and pitch for the team. That’s all that matters for me.”

“He and Lynn have done a lot to get ready for this,” La Russa said prior to Giolito’s start. “I’m sure [there are] other pitchers, top of rotation guys on other clubs that felt the responsibility to be accountable, but our guys are.”

Kendall Graveman and Dallas Keuchel made their first Cactus League appearances against Milwaukee, with Graveman throwing a scoreless frame and Keuchel allowing three runs on five hits over 2 1/3 innings with four strikeouts. Keuchel left in the sixth, but he came back to work in the seventh.

Tuesday also marked the day arbitration figures were exchanged between players and teams, although the White Sox didn’t confirm any numbers on resolutions regarding arb-eligible players in Adam Engel, Reynaldo López and Giolito. Giolito was asked about working out a contract sometime sooner than later, as he is eligible to become a free agent after ’23, but the question didn’t really specify long term or in the present contractually and Giolito gave a brief replay.

Giolito, who earned $4.15 million in ’21, answered in general terms, but slightly more extensively when a followup by the reporter pointed to him as one of the faces of the franchise.

“Yeah, the organization knows how I feel about them. Absolutely love the White Sox," Giolito said. "Love being a part of this team. I just want something fair.”