Chisenhall and Kotchman each belted a two-run homer and both delivered run-scoring hits in the decisive sixth inning, when the Indians grabbed a 9-7 lead off Sam LeCure (2-2).
Shin-Soo Choo added a solo shot and an RBI double for the Indians, who banged out 13 hits en route to a victory in the opener of their three-game Ohio rivalry series against the Reds.
Reds starter Mat Latos was pounded for seven runs on eight hits over four full frames.
Jay Bruce went 3-for-4 with a homer and two RBI while Brandon Phillips added three hits, including an RBI double, and scored three times for National League Central-leading Cincinnati, which has a six-game winning streak snapped.
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