Miles, who finished with 34 points, made eight of his treys in the first half, tying the Cavaliers' team mark held by LeBron James, Wesley Person and Danny Ferry, and surpassed it with two more in the fourth quarter.
Kyrie Irving returned from a bruised knee with 16 points and Anderson Varejao provided 18 with 14 rebounds as Cleveland won for just the second time in 10 games.
The Cavs earlier Tuesday acquired all-star forward Luol Deng from Chicago in exchange for suspended center Andrew Bynum, three future draft picks and the right to swap 2015 first-round picks with the Cavs.
Rookie Michael Carter-Williams posted a career-high 33 points for the Sixers, who fell after taking four straight road wins against Western Conference foes.
Celebrity Couples of 2014 [PHOTOS]