Brown moves to 13-24 overall and 7-11 in the Ivy League, while Yale moves to 17-24-1, 11-7.
Scott Politz went the full seven innings for the complete game as he allowed one earned run on Shulman's solo shot. Christian Taugner (Roselle, Ill.) took the loss for the Bears as the starter.
After Yale opened with three runs in the first frame, the Bears took one back in the second when Shulman blasted a homer over the left field fence.
The two teams combined for two scoreless innings, before the Bulldogs scored six runs on five hits in the fifth frame. The visitors tacked on three more runs in the top of the sixth to secure the victory.
Game 2 (Brown 7, Yale 4)
Rob Henry (Cranston, R.I.), Tim McKeithan (Arden, N.C.) and Shulman all homered in the second game. McKeithan had two hits and three RBIs, while Henry and Shulman had two RBIs apiece.
Reid Anderson (Aledo, Texas) picked up the win with one earned run over 5.2 innings of work to go along with six strikeouts. Chasen Ford gave up all seven runs on the other side for the loss.
Yale jumped out to an early lead with two runs in the first and then held the Bears scoreless over the next four frames for the two-run lead midway through the game.
Brown woke up in the bottom of the fifth, however, as Shulman and Henry blasted a pair of two-run home runs to put the home side in front, 4-2.
Yale managed to chip away with one run in eighth and another in the ninth, but Henry struck out the side to end the game and salvage the split.
Brown will wrap up the season tomorrow with a doubleheader at Yale. First pitch is set for 1 PM.