It was the fourth consecutive shutout for the Bruins in the tournament and their 15th this season, tying a school record.
With the win, UCLA (20-1-3) advanced to the women's College Cup, the Final Four of soccer, for the first time since 2000. The Bruins will face top-seeded North Carolina in a semifinal Thursday in Cary, N.C.
The No. 1-ranked Tar Heels are the only team to have defeated UCLA this season, winning, 5-2, on Sept. 19.
Penn State (19-3-3) had its season ended mainly because it had difficulty keeping up with the speedy, aggressive Bruins. Penn State goalkeeper Amanda Brown kept the outcome from being more one-sided by making three saves, and by cutting off other scoring chances before UCLA could get to them.
Whitney Jones, Iris Mora, Bristyn Davis and Kim Devine scored the goals for the Bruins.