Boston College cut a 10-point halftime deficit to 64-63 on Reggie Jackson's long, high-arcing 3-pointer with 16 seconds left. Scheyer was fouled after he received the inbound pass and made both free throws before BC's Joe Trapani put a long 3-point attempt off the front of the rim at the buzzer.
The Blue Devils (19-4, 7-2 Atlantic Coast Conference) have beaten the Eagles three straight times since BC's victory over then-No. 6 Duke last February.
Corey Raji had 15 points and eight rebounds for BC (12-11, 3-6), which has lost seven of its last 10 games.
It was the second straight payback win for the Blue Devils, who were coming off a victory over a Georgia Tech team that had beaten them earlier this season. BC upset Duke in Chestnut Hill last season, sending the crowd storming onto the court to celebrate just its second win ever over the Blue Devils. Duke plays archrival North Carolina on Wednesday.
Two nights after making 12 of 18 3-point attempts against Georgia Tech, Duke missed its first six tries from beyond the arc; the Blue Devils finished 5 of 17 from 3-point range in all. Duke, which entered the game with a nation's best 76.6 percent free throw percentage, also missed six of its first eight free throws -- and another two in the final minute -- before finishing 15 of 26 from the line.
The Blue Devils closed the first half with seven straight points to open a 35-25 lead.
Tyler Roche hit two free throws for BC to cut the deficit to 58-53 with just under 2 minutes left. But Smith drove to the basket and hit a hooking layup off the backboard and, after free throws left it 62-60 with 28 seconds left, Smith hit two foul shots to make it a four-point game.
Jackson hit a 3 to cut the deficit to 64-63 with 16 seconds left. Scheyer hit his free throws, then neither Jackson nor Trapani could get a clear look at the rim before Trapani had to fire up a shot at the buzzer.
Kyle Singler, who had a season-high 30 against Georgia Tech, was 4 of 14 from the field for 12 points.