The Red Storm (3-0) led by as many as 14 points in the first half and took a 42-32 lead into halftime.
Sean Evans scored the first three points of the second half, but the Bears (1-3) cut the lead to 57-51 with 11:49 remaining.
St. John's again built a 13-point advantage, leading 71-58 with 6:40 left. Brown then ran off a 16-4 spurt, capped by Tucker Halpern's 3-pointer, to make it 75-74 with 1:13 left.
Kennedy scored on a dunk, then Halpern hit a jumper with 41 seconds left. Malik Boothe hit two free throws with 18 seconds remaining for 79-76. Adrian Williams missed the tying 3-pointer with a second left and Boothe rebounded.