The Bears (7-6) were trailing late until Rafael Maia converted a three-point play to go up 68-67. Steven Spieth and JR Hobbie each sank a pair of free throws, but Sacred Heart's Cane Broome answered with a 3-pointer to tie it with 51 seconds left.
Blackmon hit a layup, Leland King dunked, and Blackmon hit 3 of 4 late free throws to keep Brown up by three. Tevin Falzon's half-court heave couldn't find the net for Sacred Heart (6-6) as time expired.
King finished 19 points while Blackmon, Maia and Spieth each chipped in 13 points. King and Maia grabbed nine rebounds apiece for Brown, which shot 48.3 percent from the field.
Broome paced the Pioneers with 23 points and Evan Kelley had 17.