The Trojans were locked in a 44-44 battle 7 minutes deep in the second half, but then embarked on an 8-0 run that was finished off by a Gibson slam dunk.
Gibson came within one field goal of equaling the all-time NCAA Tournament record for most baskets without a miss. He also grabbed six rebounds and blocked three shots to keep the Trojans' season going.
USC (22-12) made it into the tournament as a No. 10 seed only because it defeated three higher seeded teams in as many days last week to claim the Pacific-10 Conference Tournament title.
Dwight Lewis added 20 points for USC and DeMar DeRozan had 18.
Boston College (22-12) had a four-point lead at halftime, but could hit only 23 percent of its shots in the second period. The seventh-seeded Eagles were led by Corey Raji with 15 points.