Takia Starks scored 20 points and Danielle Gant added 14 to lead the Aggies.
Texas A&M led by 10 at halftime, 31-21, and opened up a 15-point second half lead, but Penn State mounted a comeback.
The Aggies led 46-31 before committing a series of turnovers and missed shots that fueled Penn State's comeback. The Lady Lions forced five straight turnovers at one stage, leading to nine points and cutting Texas A&M's lead to 48-46.
Penn State took a 54-53 lead with under four minutes to play.
Danielle Gant made a free throw to tie the game at 54, as Texas A&M shot 8-for-12 from the foul line the final three minutes to hold off Penn State.
Penn State guard Tyra Grant, who scored 22 points, had an opportunity to tie the game with 6.2 seconds left, but missed one of her two foul shots.
The Aggies (5-0) will play the winner of the game between host Pepperdine and Coppin State in the championship game of the four-team tournament Saturday while the Lions (3-2) will play the loser in the consolation game.