After squandering a 15-point second-half lead, Lawal hit several key free throws and had a big block in the final minute and Georgia Tech (11-2) recovered to win its third straight to move within one victory of last season's total.
Green hit seven 3-pointers in his career-best night for the 49ers (10-3), who trailed by 12 with 8 minutes left before a 17-4 run put them ahead 66-65 with 2:38 left.
But D'Andre Bell answered with a 3-pointer and Lawal hit two free throws. Up 70-66, Lawal rejected Chris Braswell in the lane and later put it away at the line.
Lawal, who was a career 54 percent free-throw shooter entering this season, hit 17 of 20 free throws and added 10 rebounds. Iman Shumpert added nine points in his first game back from knee surgery.