The Eagles (14-16, 6-11) spent most of the game battling back, then refused to let go of the lead after pulling ahead 47-46 on Anderson's layup with just under 9 minutes left.
Joe Rahon added 10 points for Boston College, which won its second straight conference game and completed a two-game sweep of Clemson. The Eagles shot 45.1 percent (23 of 51) from the field.
In their final home game for the Tigers (13-16, 5-12), Devin Booker had 19 points and eight rebounds and fellow senior Milton Jennings had 18 points and seven rebounds. Former Laney standout Rod Hall had four points, four rebounds and six assists.
Clemson has lost five in a row and eight of nine.
The Tigers, who shot 44.1 percent (26 of 59), received 11 points off the bench from Damarcus Harrison.