Batey drove from the right wing to draw the foul on A&M's Tori Scott for the game-winning free throws.
Karla Gilbert had just pulled Texas A&M even on a three-point play with 10.2 seconds left. The Aggies had previously pulled to within one point three times in the final 2:25.
Batey finished with 17 points and scored nine of Vanderbilt's last 11 points. Christina Foggie added 14 points and Jasmine Lister had 11 for the Commodores (17-5, 6-3 SEC).
Gilbert had 26 points and 12 rebounds to lead the Aggies (17-6, 7-2), and Tavarsha Scott-Williams scored 14 points and grabbed nine rebounds.
Texas A&M took its first lead at 40-39 on Gilbert's layup with 12:38 left and played back-and-forth the rest of the way.