Freshman Jackie Froatz had a career-high 16 points for the winners, while senior Diana Caramanico scored 10 points and grabbed nine rebounds. Freshman Jewel Clark scored eight of her 10 points in the game's final six minutes to help the Quakers down the stretch.
Penn's triumph followed a 92-80 overtime victory at Yale on Friday - a weekend sweep that extended the Quakers' all-time-best win streak to 11 straight.
"What a game. What a weekend," Greenberg said. "Both games, at one point, you just thought, 'Well, we just can't win it.' Then, all of a sudden someone on our team would step up and get a rebound we shouldn't have gotten, and score, and get fouled. Just unbelievable plays.
"Just the fact that the four wins we have in the league right now are all on the road is unbelievable," Greenberg added. "Because I just feel there's no way we're going to lose in the Palestra, but we still have to be ready and prepared."
Penn jumped to a 40-30 halftime lead as the Quakers were spurred by a 16-for-17 effort on free-throw attempts.
But Brown rallied at the start of the second half with a 20-9 run to take a 50-49 lead with 11 minutes, 37 seconds to play.
The Bears might have seemed on the way to another win when they held a four-point lead with just under three minutes to play. However, the Quakers' defense stiffened as they went on to score the last eight points of the game over the final 1 minute, 15 seconds.
"When we lost to Temple [in December], we were not tough," Greenberg said. "Even though we lost our next game to Villanova, I thought we were better.
"Since then, we have been very tough," she said of the current win streak.
Penn held a 45-24 advantage in rebounds, including an overwhelming 26-4 margin on the offensive boards.