Griffin blanked UAB last Friday, and suffered an injury at the end of the contest that caused her to miss the Middle Tennessee match last Sunday.
She recorded nine saves against the Tigers to notch her fifth shutout of the season and is now a shutout away from surpassing Christy Barringer (28.5) as the Commodores all-time leader.
The game was delayed for 15 minutes at the start due to rain in Baton Rouge.
The Commodores had control of the contest throughout regulation, with a 7-3 shot advantage at the half and a 19-10 lead after 90 minutes of play. The Tigers were the aggressors in the overtime periods, holding an 8-1 shot advantage.
Rachel Yepez appeared to score the game winning goal for LSU in the fifth minute of overtime but was whistled for an offside and the goal was disallowed.
Seniors Lea Lafield and Susan McAleavey had three shots on goal to lead VU, while freshman Michelle Makasini led LSU with three of her own.
LSU goalkeeper Valerie Vogler recorded eight saves including six in the second half in the Tigers fourth shutout of the year.
The Commodores will be back in action on Sunday as they take on Arkansas at 1 p.m. The Razorbacks (7-1) SEC opener against Kentucky was postponed Friday night due to lightning in the Fayetteville area.