With the Trail Blazers down by two points and time running out, Damian Lillard found Batum in the near corner and he used a single-motion catch-and-shoot to drain the decisive trey.
Batum's big 3-pointer gave him 22 for the game and Lillard tallied 24 as Portland snapped a four-contest losing streak, recording its first win while on a seven-game road trip.
Cleveland got 19 points and 17 rebounds from Anderson Varejao in its 11th loss in 13 games.
Dion Waiters injured an ankle in the second overtime after recording 12 points with seven assists for the Cavs.
2014: The Year in Music [PHOTOS]