North Carolina State, Maryland and Florida State also advanced in the tradition-rich tournament that will see the league's top seeds get into action Friday.
Hanlan made eight 3-pointers and scored 41 points. He was 14-of-18 from the field and hit his last 12 shots.
Boston College won its fourth in a row, improved to 16-16 and earned a chance at regular-season league champion Miami. The Eagles and Hurricanes will meet in the first of Friday's quarterfinal games.
Georgia Tech wasted a great start in which it scored the game's first 15 points. Boston College produced a 24-5 run late in the first half to take a 38-33 lead at the break.
In the other opening round games Thursday North Carolina State cruised by Virginia Tech 80-63, Maryland got the best of Wake Forest 75-62 and Florida State edged Clemson 72-69.
North Carolina State will meet Virginia in the quarterfinals, Maryland will take on Duke and Florida State will go up against North Carolina.
Richard Howell had 22 points and 12 rebounds in leading North Carolina State (23-9). Virginia Tech star Erick Green went just 5-of-19 for 15 points in his final game for the Hokies.
Maryland trailed Wake Forest by five at intermission, but the Demon Deacons went cold from the field during the second 20 minutes -- including a 1-of-9 effort from 3-point range.
Dez Wells led the Terrapins (21-11) with 21 points and was one of five Maryland players in double figures.
Clemson scored eight points in a row late in its meeting with Florida State to climb within three, but the Seminoles came up with four free throws from Michael Snaer over the final 23 seconds to hold on.
Okaro White scored 24 points for Florida State (18-14).