OAKLAND -- James Kaprielian has maintained that there's still another level of his game he's looking to reach at the Major League level. If these are the types of performances he brings to the mound when he's not at his complete best, it's scary to think what it might mean for the rest of the league once he does find that next gear.

After emerging as perhaps the A's biggest surprise of the first half, the rookie right-hander returned for his first start back from the All-Star break with more of the same impressive qualities he's shown all year. Kaprielian silenced the Angels' offense over six shutout innings en route to a 6-0 victory on Tuesday at the Coliseum, securing a two-game sweep of Oakland's division rivals.

And yet, after a pristine effort that featured seven strikeouts with just five hits and two walks, Kaprielian was still not fully satisfied with himself.

"I haven't quite dominated the way I want to," Kaprielian said. "I had two walks today. That just can't happen, flat out. Some of the hits I gave up were on pitches I didn't like. I do believe I'm capable of more. I can't really complain when I go scoreless, but you take it for what it is and continue to grow."

Kaprielian is no stranger to jams. Since making his first Major League start on May 12 at Fenway Park, the 27-year-old righty has found himself having to pitch through heavy traffic on the basepaths through each of his 12 starts this season. Those tough situations have allowed him to show off an impressive poise that is rarely seen out of a rookie hurler, which continued on Tuesday as he held the Angels hitless with runners in scoring position at 0-for-6 in such situations. For the season, opposing teams are batting just .136 (6-for-44) against Kaprielian with runners in scoring position.

"He's able to bear down in key moments," A's manager Bob Melvin said. "He's been as good as anybody we've had in the rotation this year in those key moments."

Consistency has also been one Kaprielian's brightest attributes. With Tuesday's scoreless performance, he's now allowed two runs or fewer in nine of his 12 starts. His ERA dropped to 2.65, which ranks as the lowest among qualified American League rookies.

When laying out the contenders for AL Rookie of the Year Award before the season, nobody could have seen Kaprielian emerging as a serious candidate. The only reason he was initially called up and placed into the A's rotation back in May was out of necessity due to multiple injuries to other starters. Now, having allowed no more than six hits in each of his 12 starts, Kaprielian is forcing his way into the conversation for that honor.

"I didn't know what to expect when he had his first start and got in trouble in the first inning," Melvin said. "Since then, it seems like every time there's some traffic out there, he ends up making big pitches. We're learning more and more about Kap as we go along here."

Kaprielian's fastball averaged 92.8 mph on Tuesday. It's a respectable velocity, but one that is significantly lower from other rookie sensations that have come through the league. What Kaprielian's fastball lacks in speed, though, is made up for with his supreme confidence in the pitch. He showed he wasn't afraid to challenge hitters with it, throwing the four-seam fastball for 47 of his 100 pitches and finishing off six of his seven punchouts with it.

Kaprielian also showed no fear going after one of the game's best. Frustrated with his four-pitch walk of Angels two-way star Shohei Ohtani in the first, Kaprielian was eager for redemption in their next encounter. The two squared off two more times in the game, and Kaprielian struck him out twice -- both times swinging -- on fastballs in the third and fifth.

"For me, it's not really about who's in the box," Kaprielian said. "Ohtani is a great baseball player. We all know that, but I believe in the guys behind me and the guy behind the dish. I believe in my stuff. It's about executing pitches. Until guys prove they can beat me, I'm going to believe in myself and make the pitches."

Matt Olson provided Kaprielian an early run of support by mashing a solo shot off José Suarez in the fourth. The homer was his 25th of the year and marked his second straight game with a home run.

Once Kaprielian departed, the A's offense broke out with three runs in the sixth and two more in the seventh. Of the five late runs, four came on two-out hits. For a club that started off a five-game homestand struggling with situational hitting, Tuesday's offensive outburst can be viewed as a good omen as the club enters an off-day on Wednesday before embarking on a 10-game road trip that begins Thursday night in Seattle.

"We got our best at-bats towards the latter innings, which was good to see," Melvin said. "It's a trait we've always had. Our at-bats seem to get better as the game goes along. That was the case today."