Pulliam stopped senior Rachel Wood on the opening attempt, lunging to her right to stone Wood for the second time in as many PK attempts (Wood was denied in the 96th minute of a 0-0 regular-season-ending tie with visiting Hawaii on Sunday).
After Kishi Smith converted for the Titans, Pulliam turned away UCI's Jenna Pellegrino, lunging to her right once again.
Chelsey Patterson knocked in the second PK for Fullerton, before Pulliam dived to her left to stop a low shot from Devon Delarosa.
Stacey Fox drilled the ensuing penalty kick to spark a celebration for the Titans.
The loss eliminates the No. 4-seeded Anteaters (9-8-4) and, barring a surprise, ends their season, as well as a run of two straight trips to the NCAA Tournament. The game is recorded as a tie, with the penalty kicks deciding which squad advances.
It was the third season the Anteaters have fallen in the conference tournament. But the past two years, they were granted at-large berths into the NCAA Tournament after impressive regular-season results that included back-to-back conference crowns.
So, despite having lost only two regular-season matches the last three seasons, UCI, with a Ratings Percentage Index of 59, figures to be sitting out this season's NCAA Tournament.
Fullerton, which claimed its first conference regular-season title since 2007, will face Cal State Northridge in Sunday's 1 p.m. final at UCI. The Matadors earned the program's first Big West Tournament win with a 1-0 triumph over Cal Poly San Luis Obispo at UCI earlier Thursday.