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Oakland Athletics starting pitcher Adrian Martinez (55) delivers against the San Francisco Giants during the second inning of a baseball game, Sunday, Aug. 7, 2022, in Oakland, Calif. (AP Photo/D. Ross Cameron)

OAKLAND, CALIFORNIA - AUGUST 07: Tony Kemp #5 of the Oakland Athletics catches a ball hit by Mike Yastrzemski #5 of the San Francisco Giants, while almost colliding with Skye Bolt #11, in the fifth inning at RingCentral Coliseum on August 07, 2022 in Oakland, California. (Photo by Ezra Shaw/Getty Images)

OAKLAND, CALIFORNIA - AUGUST 07: Sean Murphy #12 of the Oakland Athletics slides into third base in the fourth inning against the San Francisco Giants at RingCentral Coliseum on August 07, 2022 in Oakland, California. (Photo by Ezra Shaw/Getty Images)

Oakland Athletics third baseman Vimael Machín (31) leaves his feet as he throws too late to get San Francisco Giants' J.D. Davis at first on an infield single during the seventh inning of a baseball game, Sunday, Aug. 7, 2022, in Oakland, Calif. (AP Photo/D. Ross Cameron)

Oakland Athletics infielder Tony Kemp (5) fights the sun as he makes the catch of a fly ball by San Francisco Giants' Luis Gonzalez during the seventh inning of a baseball game, Sunday, Aug. 7, 2022, in Oakland, Calif. (AP Photo/D. Ross Cameron)

OAKLAND, CALIFORNIA - AUGUST 07: Seth Brown #15 of the Oakland Athletics is congratulated by Jonah Bride #77 after he hit a home run in the eighth inning against the San Francisco Giants at RingCentral Coliseum on August 07, 2022 in Oakland, California. (Photo by Ezra Shaw/Getty Images)

Adrián Martínez rejoined the Oakland Athletics this weekend with no assurances. Frankie Montas’ exit left an open spot in their rotation. Martínez arrived with the first chance to claim it. His status, manager Mark Kotsay said Sunday morning, would likely be gauged start-to-start.

For a last-place A’s team, the next two months figure to involve evaluating players for the future. One example is Martínez, the 25-year-old right-hander Oakland acquired from San Diego for Sean Manaea this spring, who’s among several starting pitchers who could vie for time with the A’s down the stretch.

In a 6-4 loss to the Giants on Sunday, Martínez worked quickly and avoided some of the command issues that marked his previous A’s starts. He paid for one mistake, an 0-2 fastball that Mike Yastrzesmki hit for a homer, departing a 1-0 game in the fifth inning after two trips through the Giants’ lineup.

“We’re working with Adrián on his mechanics ... and I think he’s made a little bit of improvement,” Kotsay said. “The slider had more depth, it wasn’t side-to-side. The changeup as well. Fastball had life to it and some sink. So I think he’s moving in the right direction right now and that, for us, is a good sign.”

Martínez’s sinker has low-to-mid 90s velocity, requiring sharp command to avoid hard contact. Hitters were 17-for-50 with five homers against the sinker in his first four A’s starts, which produced a 6.52 ERA. Four walks in his last outing, July 11 in Texas, spoke to shaky control.

Sunday, Martínez used his off-speed pitches more and to effect. Martínez’s changeup is said to be his best pitch. Giants hitters swung at 20 of 24 he threw and missed eight. The 12 pitches Giants hitters put in play against Martínez averaged an 83.1-mph exit velocity — 95 mph is considered hard-hit.

Martínez threw 48 of 69 pitches for strikes, walking one and striking out five. He pitched with pace early, hopping off the mound after a strikeout of Brandon Crawford to finish his second inning. There were also slips. In the third, Martínez left an 0-2 sinker over the plate for Yastrzemski, who hit it 409 feet. Martínez exited after allowing two singles in the fifth inning, one of those runners scoring after he left.

“I thought he looked so much better today,” catcher Sean Murphy said. “Pitching with more confidence, I think.”

The A’s were already cycling starters through their fifth rotation spot before the trade of Montas to the Yankees opened another. Adam Oller, who like Martínez has bounced between Triple-A and Oakland, is currently in the A’s rotation and Kotsay said: “There may be more guys included in that as we go forward.”

“It’s just another opportunity for me,” Martínez said through a translator. “I’m just going to take advantage of it and continue to work and hopefully I continue to be here.”

Matchup game: The Giants got the better of the A’s in a couple of matchup maneuvers. Kotsay replaced Martínez in the fifth with left-hander Sam Moll. Giants manager Gabe Kapler pinch-hit for left-handed Joc Pederson with right-handed Austin Slater, who lined an RBI double over the head of left fielder Tony Kemp.

Oakland deployed left-hander A.J. Puk for the sixth. The Giants pinch-hit right-handed Wilmer Flores for left-handed LaMonte Wade Jr. Flores drew a walk, then Puk allowed a homer to Thairo Estrada on an 0-2 pitch.

“He’s trying to go up above the zone, get a swing and miss,” Kotsay said of Puk. “He missed middle and we paid the price for it. ... You saw (on Saturday) we went up a lot with Oller but went too high where we didn’t get the swing and chase. So there’s a fine line to it.”

On offense: Hitless against Logan Webb until the fifth inning, the A’s offense stirred in the later innings. Vimael Machin, who entered with a .194 average, doubled for their first hit and scored on a Skye Bolt single. Machin also walked to begin the A’s seventh and later scored on a fielder’s choice.

Seth Brown drove a two-run homer in the eighth inning. Facing hard-throwing Giants closer Camilo Doval in the ninth, the A’s put two on with one out but continued a daylong trend of not delivering the clutch hit. They finished 1-for-14 with runners in scoring position and left 10 men on base.

Briefly: The A’s optioned infielder Dermis Garcia to Triple-A Las Vegas before the game to clear a roster spot for Martínez. ... The A’s have not hit a triple in 69 games, the longest such streak by an AL or NL team since at least 1901. ... Brown’s homer was his seventh in 12 games since the All-Star break. ... Reliever Dany Jiménez worked a scoreless inning with two strikeouts in his second outing since returning from the IL.

Matt Kawahara covers the A’s for The San Francisco Chronicle. Email: mkawahara@sfchronicle.com. Twitter: @matthewkawahara