The Athletics seek a fourth straight win overall and a six-game run against the Indians on Tuesday night.
After dropping eight of its first 13 games this month, Oakland (70-57) has won nine of 11 since, including three straight. The Athletics are 4-0 against Cleveland in that stretch, taking Monday's series opener 3-0 for their second consecutive shutout in the series.
Brett Anderson was superb in his second start since having Tommy John surgery in 2011, yielding two hits in seven innings.
Cleveland (55-73), which is scoreless in 36 of its last 39 innings, isn't the first opponent to be on the other end of a solid pitching performance by Oakland, which has the AL's second-lowest ERA (3.46). The Athletics have a 2.66 ERA over the last 11 games, with the number slightly skewed by a 7-2 loss to Minnesota on Aug. 20.
Oakland, a major league-best 33-15 since the start of July, is tied with Baltimore for the first AL wild-card spot and one-half game ahead of Tampa Bay for the second.
The Indians, meanwhile, have lost 11 of 12 and are averaging 2.5 runs and batting .214 in those games. They have struck out at least 10 times in three of the last four, with the top three batters in their order Monday going 0 for 11 with five strikeouts.
"This is frustrating," third baseman Jason Donald told Cleveland's official website. "It's not enjoyable losing ballgames like this, especially when you feel like you have a chance to win it. It just seems like it keeps piling on right now."
Oakland hasn't won six straight in a single season against Cleveland since 1998, when it posted an eight-game streak in the series.
The Athletics will try to move 14 games over .500 for the first time since they finished the 2006 season 93-69 with Tommy Milone (10-9, 3.87 ERA) on the mound.
Milone earned his first win in more than a month after limiting Minnesota to one run and two hits over eight innings of a 5-1 victory last Wednesday.
The left-hander, who was winless in his five previous starts, had a 7.50 ERA over the four prior outings.
"That's about par for what he's done at home through the season," manager Bob Melvin said. "It was a great outing, a nice recovery."
Milone surrendered four runs and seven hits over five innings against the Indians on Aug. 17 before leaving without a decision in a 6-4 win.
Zach McAllister (5-4, 3.50) opposed Milone in that start and also didn't receive a decision after allowing four runs and eight hits in six innings.
The right-hander is 3-2 with a 3.21 ERA at home this year. He hasn't given up more than three earned runs in any of his nine starts at Progressive Field.