Batum's cool effort snatched a 118-117 success, while Damian Lillard top-scored with 24 points.
Alonzo Gee contributed 22 points for the Cavaliers but missed a vital three-point shot moments before Batum's winner.
The San Antonio Spurs defeated Southwest rivals Memphis Grizzlies 99-95 in overtime.
Tony Parker poured in 30 points and Tim Duncan coupled 27 points with 15 rebounds in a high-quality match that saw Marc Gasol lead the Grizzlies with 22.
The Miami Heat went 12-3 for the season with a 102-89 victory over the Brooklyn Nets.
Dwyane Wade's 34 points did much of the damage, with LeBron James adding a further 21 as the Nets saw a five-game hot streak come to an end.
The Houston Rockets were 124-116 winners over the Utah Jazz, making it five home wins in a row.
Rockets trio Patrick Patterson (20), Chandler Parsons and Jeremy Lin (both 19) all scored well, but Gordon Howard led the way in a losing cause for the Jazz.
Oklahoma City Thunder eased their winning run out to five matches as they brushed off the New Orleans Hornets 100-79.
After compiling a 27-point advantage the Thunder took their feet off the pedal in the last stanza, leaving Kevin Durant as top-scorer with 20 points.
Ryan Anderson had 21 points and 10 rebounds for the Hornets but was wayward from distance as his side made it nine losses from their last 10 attempts.
The Dallas Mavericks claimed a straightforward 92-77 win over the Detroit Pistons, the Milwaukee Bucks edged the Boston Celtics 91-88 and the Golden State Warriors defeated the Indiana Pacers 103-92.
Luol Deng's 25 points was the best of the match as the Chicago Bulls fashioned a 93-88 success over the Philadelphia 76ers.
The LA Clippers crushed the Sacramento Kings 116-81, with seven of the winning team's players scoring in double figures.