With the win, the Bears completed a sweep of both Penn and Princeton in the same season for the first time since the Ivy League formed in 1954.
Brown (17-9, 9-3) also tied the school record for most wins in a season which is held by the 1974, 2003 and 2004 teams.
The Bears' Damon Huffman sank two 3-point shots in the game which gave him 216 for his career and broke the school record of 215 set by Brian Lloyd from 1992 to 1996.
Brian Grandieri with 16 was the only player to reach double figures for the Quakers (11-17, 6-5), who had won four of their previous six games. The 32-point loss was Penn's worst against Ivy League competition, eclipsing a 26-point loss to Princeton in 1968.
Brown broke the game open early by running out to a 14-0 lead and holding Penn without a basket for the first 7:21.
The Bears led 44-14 at halftime and increased the lead to as many as 39 points twice in the second half, the last time at 58-19.