Fair connected on 12-of-20 shots from the field en route to his career-high total and Jeremi Grant added a personal-best 24 points with 10 rebounds as the Orange (21-0, 8-0 ACC) remained undefeated.
Syracuse posted the victory in front of 35,446 fans at the Carrier Dome -- the largest on-campus crowd in NCAA basketball history.
The Blue Devils (17-5, 6-3) stayed in the game by nailing 15-of-36 tries from 3-point range.
Rasheed Sulaimon forced overtime with a 22-footer at the buzzer, part of a 16-point effort.
Jabari Parker added 15 points with nine rebounds and Amile Jefferson provided 14 and seven before each fouled out in the final 2 minutes of regulation.
Duke had its five-game winning streak snapped.