Syracuse led by seven points with 70 seconds remaining before the bottom fell out.
Kameron McGusty made a pair of jumpers and Miller added a pair of buckets, including a tip-in to give Miami a 73-72 lead. Miller grabbed the rebound and made two free throws after he was fouled with 3.9 seconds left.
On Syracuse's final possession, Jimmy Boeheim was short on a 3-pointer that would have sent the game to overtime.
It was the second time this season that Miami rallied from an 18-point deficit to beat Syracuse. The Hurricanes overcame an 18-point deficit in the first half of their 88-87 win over the Orange on Jan. 5.
Miller finished with 25 points and 13 rebounds for the Hurricanes (22-9, 14-6 Atlantic Coast Conference), who improved to 10-2 on the road. He made 10-of-13 shots and 5-of-5 on free throws.
Kameron McGusty scored 19 points and Isaiah Wong added 15 for Miami.
Boeheim led Syracuse (15-16, 9-11) with 30 points.
The Orange, who fell to 11-5 at home this season, also got 17 points from Girard and 14 from Jimmy Boeheim.
Syracuse led 37-26 at halftime, thanks to 6-for-12 shooting on 3-pointers and an 8-2 edge on second-chance points. Miami made just 1-for-11 on 3-pointers, and the Hurricanes gave up an 11-1 run midway through the first half.
Buddy Boeheim led all first-half scorers with 18 points on 5-for-10 shooting, including 3-for-6 on 3-pointers.
In the second half, Syracuse extended its lead to 18 points, but a 13-0 Miami run cut the Hurricanes' deficit to 44-39 on Charlie Moore's layup with 14:11 left. Moore had three layups during that run.
Miami then used a 6-0 run — a spurt that included a 30-foot lob pass that ended in Wong's spectacular dunk — to cut the deficit to 62-58 with 4:34 left.
In the final minute, Miami got two jumpers in the lane from McGusty, two Miller tip-ins and the two Miller free throws.