Duke (27-6) led only 44-41 before Gerald Henderson's 3-pointer with 8:53 started the 12-2 run. Scheyer and David McClure each had back-to-back baskets in the run, which ended with Duke leading 56-43 with 5:35 remaining.
Duke will be trying to win the ACC tournament for the fourth time as a No. 3 seed. The Blue Devils also were No. 3 seeds when winning the title in 1988, 2003 and 2005.
Maryland, playing in its first semifinal since winning the tournament as a No. 6 seed in 2004, was an even bigger underdog as a No. 7 seed this year.
The Terrapins' underdog role was especially obvious against Duke, which swept two games in the regular season, winning by double figures each time. The Blue Devils crushed the Terrapins 85-44 in Durham, N.C., and completed the regular-season sweep with 78-67 win at Maryland.
The third meeting between the teams was close until late in the game.
There were nine lead changes and three ties in the first half, with Duke taking a 32-30 lead at the break. Singler had 12 points in the first half, including two of Duke's six 3-pointers.
Maryland took a brief 34-32 lead in the second half, before a 3-pointer by Scheyer gave Duke the lead for good.
Scheyer and Nolan Smith, who finished with 10 points, combined to make six of eight free throws in the final minute to protect the lead.