McCoy finished 17 of 24 with 199 yards, despite being battered throughout much of the contest.
For the Jaguars, Blaine Gabbert had his finest game as a starter, finishing 22 of 41 with several dropped passes.
Gabbert led a fantastic drive in the closing moments, but his attempt at the comeback failed as Jason Hill dropped what would have been the game winner with three seconds left.
Jacksonville falls to 3-7, and Cleveland improves to 4-6.
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