Detroit lost right-hander Max Scherzer after only two innings to fatigue in his throwing shoulder, but an MRI revealed no structural damage.
The Chicago White Sox beat Kansas City to remain three games ahead of Detroit atop the division, taking something away from Cabrera's big night.
"Our job is to win games. There's no talk about personal numbers," Cabrera said. "Hopefully we can get a good winning streak."
Cabrera now leads the American League with a .333 average and 129 RBIs. He also has a career-high 40 homers -- two behind Josh Hamilton for the top spot.
The last Triple Crown winner was Carl Yastrzemski in 1967.
"That's a hard thing to do. You've got to be lucky," Cabrera said. "Hopefully we get lucky in our division and win more games."
Prince Fielder and Jhonny Peralta added home runs for the Tigers. Darin Downs (2-1) pitched 2 2-3 scoreless innings for the win in relief of Scherzer.
Oakland rookie A.J. Griffin (6-1) lost for the first time in his career.
"Just wasn't executing pitches the way I usually do," Griffin said. "Wasn't pounding down in the zone, leaving pitches up and they capitalized on it."
Scherzer entered the game with a major league-leading 220 strikeouts and added four more to that total before leaving after only two innings. He's expected to go a couple days without throwing, then be evaluated again.
"I didn't have any pain in my shoulder -- it was just like my arm was dead," Scherzer said. "MRI came back negative. All the structural -- it's all good."
After a gut-wrenching 5-4 loss to the White Sox in Chicago on Monday, the Tigers were back home, where they've now won 27 of 35. They'll play their next nine games at home before going on the road for the final six.
Griffin was the only pitcher since at least 1918 to allow three runs or fewer and walk two batters or fewer in each of his first 11 career starts. That streak came to an end Tuesday. He allowed five runs and eight hits in 4 2-3 innings, walking one and striking out three.
Oakland took the lead in the first on an RBI single by Brandon Moss, but Detroit answered immediately with Cabrera's sacrifice fly.
Peralta gave the Tigers a 2-1 lead in the second with his 12th homer of the year, and Cabrera hit a solo shot of his own the following inning.
Fielder's 27th homer of the year -- a two-run shot in the fifth -- made it 5-1, and the A's never made much progress against the Detroit relievers. Oakland came in three games behind first-place Texas in the AL West, but leading the wild-card race. This 10-game swing to Detroit, New York and Texas is their last trip of the regular season.
Austin Jackson hit an RBI double in the sixth for Detroit, and Quintin Berry added a two-run double to make it 8-1. Berry left in the top of the seventh with a right shoulder contusion after a diving attempt to catch Josh Reddick's double. X-rays were negative.
Reddick scored on a single by Yoenis Cespedes.
Oakland outfielder Coco Crisp started after having been out since Saturday. He'd missed time because of an allergic reaction in his left eye, and he left this game in the fourth because of complications to an existing eye infection.
Detroit added four more runs in the eighth on Cabrera's grand slam. Oakland reliever Jesse Chavez was then ejected for hitting Fielder with a pitch.
NOTES: Detroit C Alex Avila did not play and is day-to-day. He's still recovering after colliding with Fielder on Sunday chasing a pop in Cleveland. He's been bothered by headaches. His replacement, Gerald Laird, had three hits. .. Moss had three hits for the A's. ... Detroit RHP Justin Verlander (14-8) takes the mound Wednesday night against Oakland LHP Brett Anderson (4-1).