But the Broncos managed just one field goal over the next 8 1/2 minutes, and that gave Duke just enough of an opening to break open this one.
Curry hit two 3-pointers and followed with three layups during the 26-5 run that gave the Blue Devils a bit of breathing room. Quinn Cook's steal and layup capped the burst and made it 67-50 with 8:30 to play.
Curry, who was 12 of 18 from the field with four 3s, finished with his best scoring day as a Blue Devil but came up short of the 35 he scored against VMI while a freshman at Liberty in 2008-09.
Ryan Kelly had 10 points and 11 rebounds, and Cook finished with 15 points for Duke. Playing for the first time in nine days and just the fifth time in December it wasn't anywhere near its best for much of this one.
The Blue Devils missed 10 of their first 18 free throws, had six shots blocked and regularly were outworked by the Broncos. But they were good enough when it counted to make it to 12-0 for the 10th time under coach Mike Krzyzewski and win their 101st straight nonconference game at Cameron Indoor Stadium.