Meantime, UA ace Jennie Finch struck out 14 and pitched a three-hitter to win her fifth game in eight days and help the Cats stretch their home-field winning streak to 35 games. Finch improved to 19-0 and tied her career high in strikeouts.
Bauer's towering shot down the right field line drove in three runs and gave the Cats the final margin with a 7-0 lead in the fourth inning.
The Cats' 100th home run of the season, which tied Arizona's own national record set by the 1995 team, was a three-run liner to left by freshman Mackenzie Vandergeest and gave Arizona a 4-0 lead in the second inning. All four runs were unearned off SU starting pitcher Maureen LeCocq (12-5) after a two-out fielding error by second baseman Kim Ching allowed UA to continue a rally.
Three Stanford pitchers held Arizona to only three hits but the home runs followed a walk and an error in the second and a walk and a hit in the fourth. Bauer hit her home run off the first reliever, Jaime Forman-Lau.
SU collected a single by Robin Walker in the third, and later a double by Jenni Shideler and a single by Michele Thiry to threaten in the top of the seventh, but Finch struck out pinch-hitter Jessica Draemel to end the game.
Stanford dropped to 40-6-1 overall and 7-3 in conference play. Arizona improved to 44-4 and 6-2. The sixth-largest crowd in Hillenbrand Stadium history, 2,379, was on hand.
The Cardinal travels to Tempe for games Saturday and Sunday at Arizona State. Arizona plays against California at 7 p.m. Saturday and at 1 p.m. Sunday.