Senior Trevor Herrera made five saves for the Lions, whose 18 shots were one better than the Falcons' total.
Notre Dame goalie Alex Klein did not make a save.
Steven Kane converted an assist from Luke Holmes to pull the Falcons even.
Erik Beattie scored with a header near the right post with an assist from Jacob Child to propel the Falcons into Wednesday's quarterfinals.
It was only the second loss on the field all season for Vanguard, which forfeited six games after a 5-0-1 start, due to Coach Randy Dodge neglecting to sit out after having received a red-card ejection in the final game of the 2009 season.
The Lions responded to claim their first outright Golden State Athletic Conference title. They then won the GSAC Tournament crown by topping Azusa Pacific in the final.
Vanguard knocked off APU again, 2-1 in overtime, in the first round of the NAIA Tournament on Nov. 20.
Senior Tomislav Colic had four shots for the Lions, for whom sophomore scoring leader Kevin Cornwall had two. Vanguard had just two shots on goal.
Cornwall, the GSAC Player of the Year, finished with 16 goals and three assists.
Vanguard, which had won 11 straight, outscored its opponents, 59-16, this season.
— From staff reports