Mikey Thompson added 10 points for Boise State (10-2), which will play No. 14 Iowa State (10-0) in Wednesday's championship.
Brenton Williams led the Gamecocks (3-6) with 14 points and Duane Notice added 13.
Drmic scored 21 points in the first half and looked to be on pace to match his career high of 34 points.
The Broncos built a double-digit lead just nine minutes into the game. Boise State scored from all directions, driving into the lane for layups and hitting 3-pointers. Boise State forced 11 first-half turnovers and converted that into 12 points.
Boise State led 43-28 at halftime and pulled away in the second half as South Carolina struggled to find the basket, shooting just 37 percent.