Oakland scored twice in the seventh and four times in the eighth, erasing 2-0 and 3-2 deficits to extend its winning streak to six. The A's lead the AL wild-card race by a game over Boston.
"It happened last year and it's happening again, our best at-bats have been in the seventh inning on," Oakland manager Bob Melvin said. "Elvis continues to find a way to help us win games and that was another big hit by Jed."
Andrus opened the eighth with a tying homer off Nick Sandlin (1-1), who faced three batters and allowed three runs before departing with shoulder tightness.
On Tuesday, Lowrie also had the decisive RBI by doubling in Andrus in the 10th inning of a 4-3 victory. The Athletics have won seven straight in Cleveland, dating to 2018.
"Late in games, you just have to know who you are as a hitter and look for a pitch you can handle," Lowrie said. "Everyone in this lineup is a pro and I've been really impressed by Elvis this season."
Marte went 2 for 5 with his 31st stolen base, keeping his average at .400 in 11 games since joining Oakland in a July 28 trade with Miami. Andrus and Matt Chapman had two hits apiece.
"It's a tough loss, no doubt," Indians acting manager DeMarlo Hale said. "The big blow from Lowrie again. Hopefully, the timely hitting will start to come and we can stay away from the big blows that change the game."
The Indians went ahead 3-2 in the seventh when Myles Straw walked with two outs, then scored on Oscar Mercado's double to the wall off Diekman.
Converted reliever Quantrill worked six-plus innings, allowing two runs on three hits with five strikeouts. The right-hander is 2-0 with a 1.25 ERA over his last six starts, covering 36 innings.
"The biggest thing for me is knowing I'm a starter," Quantrill said. "I just attack, attack, attack the zone. I'm pitching better and executing better."
Montas gave up two singles in the first and no hits over the next five frames. The righty struck out six in six innings, giving him 51 whiffs in a 37 2/3-inning span covering six starts.
Oakland is 2-0 on a 10-game trip that includes three games against the Rangers and four with the White Sox.
The first pitch was delayed by 50 minutes by rain.
"It's Cleveland," Melvin said, smiling. "Very rarely do you not get some sort of weather delay."
Indians RHP Aaron Civale, who has been on the injured list since June 22 with a sprained right third finger, threw off the mound at Progressive Field earlier in the day. Hale said Civale will likely throw a simulated game this weekend. Civale was the first pitcher in the majors to reach 10 wins this season, beating Baltimore on June 16, but was hurt in his next start against the Cubs at Wrigley Field.
Athletics: 2B Josh Harrison (left hand bruise) was not in the lineup and is expected to sit out the series finale. Harrison was struck by a Triston McKenzie pitch on the top of his hand in the sixth inning Tuesday.
Indians: OF Harold Ramírez (right knee tightness) pulled up lame while attempting to steal second base in the first inning and exited the game. Ramírez was tagged out by Lowrie well in front of the bag.
Athletics: RHP Chris Bassitt (11-3, 3.19 ERA) ranks first in the AL with 144 innings and a .786 winning percentage. The University of Akron product shares the league lead in victories with Toronto's Hyun Jin Ryu.
Indians: RHP Eli Morgan (1-4, 6.09 ERA) made his MLB debut on May 28 and has lowered his season ERA in all eight subsequent starts. Morgan worked a career-high seven innings against Detroit on Aug. 7.