If both teams win out, there will be a one-game playoff next weekend at a neutral venue that has yet to be determined by the league office.
It would be the second year in a row that the conference's automatic bid has been determined by a playoff. Last season, Princeton beat Harvard to claim the bid.
If Harvard loses Saturday night at Cornell, Penn will be able to win outright by beating Yale on Saturday and Princeton on Tuesday. But if Harvard beats Cornell and Penn loses either of its remaining games, the Quakers will get nothing.
Penn's victory over Brown (8-22, 2-11 Ivy League) certainly did not come easily. The Quakers trailed at halftime, 24-22, and struggled throughout the second half to pull away from a resilient Brown squad.
But Rosen took over down the stretch with a series of midrange jumpers, and Miles Cartwright added two key baseline layups to keep the Bears at bay.
"One may think that at 2-10 in the league, [Brown] may slow it up and pack it in, but they did an excellent job of competing and playing hard, playing together," Penn coach Jerome Allen said. "I wasn't surprised."
Tyler Bernardini also contributed some key plays down the stretch, diving for loose balls and hitting two free throws in the final 30 seconds to seal the victory.
"We're in the month of March, and I expect it," Allen said of Bernardini's performance.
Saturday's game against Yale will be big because of the title implications, but also because it will be the final game at the Palestra for Rosen and Bernardini. Rosen admitted that it will be an emotional night.
"I don't know what's going to happen at 7 o'clock [Saturday]," he said.
"I'm going to try not to cry, though."