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 in a row 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.
In a game both teams shot under 38 percent from the field, Georgia Tech appeared in control up 15 early in the second half and 61-49 with 8 minutes left before Green's scoring burst. He hit a 3-pointer while Brian Oliver fouled Phil Jones while he was setting a screen. Jones missed the front end of the 1-and-1, but Charlotte got the rebound and Green buried another 3.
Green's layup off a turnover cut the lead to 61-57 with 5:39 left. With Georgia Tech held to 2 points in nearly 5 minutes, Charlotte tied it at 63 on DiJuan Harris' two free throws with 3:25 left, then went ahead 66-65 on Harris' 3 with 2:38 left.
The crowd went into a frenzy, but Charlotte couldn't sustain the lead playing a rare on-campus home game against a school from a major conference. Lawal and Derrick Favors, who was held to six points and seven rebounds in 23 foul-plagued minutes, were able to contain Charlotte big man Shamari Spears.
Entering averaging 17.8 points, Spears didn't get his first field goal until early in the second half and was held to eight points and four rebounds.
Georgia Tech's depth was given a boost from Shumpert, who had missed the past six games following surgery to repair damaged cartilage in his right knee. He didn't start but entered before the first timeout and quickly had a putback that started Georgia Tech's 17-2 run to take a 19-8 lead.