CHICAGO -- The shelf life for focusing on Dylan Cease’s All-Star snub unofficially ended this past Wednesday, the day after the American League beat the National League in Los Angeles.

Now, the ace of the White Sox staff has even loftier targets ahead: An AL Cy Young Award, an AL Central title for the team and extended postseason success. The right-hander took a step in the right direction for the first two goals in pitching Chicago to a 6-3 victory over the Guardians on Sunday afternoon at Guaranteed Rate Field.

People have marveled at Cease’s dominance for most of the season, as he's logged four double-digit-strikeout performances and eight starts with at least five innings pitched and less than three hits allowed. But Sunday’s effort against the Guardians (48-46) once again highlighted his mound maturity.

Cease (10-4) allowed seven hits over six innings, striking out four to once again give him the Major League strikeout lead with 154. He allowed at least one baserunner in five of those six innings, pitching with a runner in scoring position during four of them. But the Guardians never scored until Franmil Reyes’ two-run home run off Kendall Graveman in the eighth and Steven Kwan’s long ball in the ninth against Liam Hendriks.

“Any time I can hold them scoreless, it’s obviously ideal,” Cease said. “They did a good job adjusting from my last start against them.

“They put the ball in play a lot more. I just had to find other ways to get outs. This game was definitely more, in my mind, an offensive and defensive win than it was my pitching, but obviously it all goes together.”

The White Sox (48-48) cleared the fence three times, on a two-run shot from Leury García and a three-run blast from AJ Pollock during a five-run second against Shane Bieber, as well as Eloy Jiménez’s solo drive in the sixth. They raised their record to 8-0 this season in games where they have three or more home runs. The White Sox are 34-24 when hitting at least one home run.

On paper, this finale of a split four-game set looked to be a battle of the aces, with Bieber having thrown a 95-pitch complete game against the White Sox during his last start on July 12 in Cleveland. While neither pitcher had his best slider -- with Cease recording six swings and misses on the pitch, per Statcast -- Chicago's starter stayed out of trouble.

“Five runs early against one of the better pitchers around. Again, it’s all you can ask for,” Cease said. “It gives me some room to breathe, a little more confidence to go right after them.”

As for that Cy Young Award, Cease is certainly building his résumé. He is 6-2 with a 0.42 ERA over his past 11 starts, yielding three earned runs in 64 innings with 83 strikeouts and a .179 opponents average. Cease is 2-2 with an 0.49 ERA (two earned runs in 36 2/3 innings) over his past six home starts, and he has a 6-2 mark with a 1.39 ERA over nine starts against the AL Central this season.

Cease’s scoreless innings streak sits at a career-high 20 2/3 innings, and he has not allowed a run since the fourth inning on July 7 against Detroit. The White Sox finished 10-9 in this stretch of 19 straight against the AL Central, with Cease picking up three of the 10 victories.

“I'll tell you what, man, I'm still trying to figure out how that kid didn't make the All-Star team,” Cleveland manager Terry Francona said. “He's one of the best pitchers in the game. He didn't quite have the wipeout slider today that he had the other day, thank goodness. He's still a handful."

There was no All-Star Game viewing for Cease during what he told reporters was “a nice little break.” Cease knows his first-half statistics matched up against any hurler in baseball, but that All-Star oversight can become a little extra motivation in looking at his 13 or 14 starts over the remaining 66 games.

“Just trying to win is enough motivation for me,” Cease said. “But I’ll take any chip on my shoulder I can get.”

“He wanted to go. You can't doubt his credentials. But that process is there,” White Sox manager Tony La Russa said. “Every year, somebody misses. But he handled it. He just kept pitching. He's happy, he pitches. Disappointed, he pitches. He's an old pro at a young age."