Carmona (3-0) scattered seven hits, didn't allow a walk and struck out four en route to the victory while Austin Kearns collected three hits and drove in three runs in the Indians' win, just their fourth in 26 road games going back to 2009.
With the score tied 1-1 entering the eighth, Oakland reliever Chad Gaudin (0-2) gave up a lead-off single to Matt LaPorta. After Grady Sizemore came in as a pinch-runner, Mike Redmond sacrificed him to second. One out later, Grudzielanek stroked the game-winning single to center.
Redmond added two hits and scored twice for the Indians.
The A's lone run was driven in by Cliff Pennington with an RBI single.