The Indians will now try to hand Tommy Milone a career-worst fourth straight loss.
Cleveland could also move a season high-tying two games above .500 on Tuesday night when this four-game series continues at Progressive Field.
Asdrubal Cabrera had a career high-tying two homers, Mark Reynolds' AL-leading 10th home run went an estimated 460 feet and Jason Kipnis added a solo shot as the Indians (15-14) won Monday's opener 7-3.
Cleveland, the AL leader with 44 home runs, had dropped five in a row at Progressive Field to the A's (18-15) and eight in a row overall in since a 5-1 road win last April 12.
The Indians, winners of seven of eight, can now move two games above the break-even point for the first time since opening 2-0 with a pair of victories in Toronto.
Milone (3-3, 3.69 ERA) will try to prevent that from happening and halt his personal three-start skid. The left-hander, though, can't be solely blamed for his recent results, as the A's have totaled five runs in his losing streak after plating 28 in his first three.
Milone takes the ball for the first time since surrendering a career high-tying three home runs in Wednesday's 5-4 loss to the Los Angeles Angels. The southpaw also struck out 10 - matching a career high - and walked none in seven innings.
"I wanted to go as deep into the game as I could,'' Milone said. "The bullpen has been out there a lot the last few days. I needed to go out and throw strikes. I felt good throughout the game, it was just a few bad pitches.''
Milone is 1-0 with a 3.27 ERA in two starts against Cleveland, both coming last season.
Scheduled starter Zach McAllister (2-3, 3.30) was on the mound for the Indians in both of those contests, going 0-1 with a 7.84 ERA after giving up five runs in a 7-0 home loss on Aug. 28.
The right-hander has lasted five or more innings in all five starts this season, giving up three earned runs or fewer each time. McAllister picked up his second victory of the season last Tuesday when Cleveland hit a season-high seven homers in a 14-2 victory over Philadelphia.
"That was a lot of fun," he told the Indians' official website after going seven strong innings. "I think any pitcher will tell you they're happy to have offense like that, and they'd gladly have more time in the dugout with longer innings than not having any runs and going out there to try to pitch."
McAllister could be spending plenty of time in dugout, as the Indians are batting .344 and averaging 7.8 runs during their 7-1 run.
AL player of the week Ryan Raburn is hitting .560 (14 for 25) with four homers and 10 RBIs in his last six games after driving in a run on Monday.
Raburn, though, is hitless in three at-bats off Milone.
A's center fielder Yoenis Cespedes, who could match a career high by homering in a third straight game, is 2 for 6 with a double versus McAllister.