Payne made 7-9 field goals and led all rebounders with 13 while blocking five shots to go with 14 points. The Auburn center was also a star on defense. She held Buffalo's leading scorer, Heather Turner, scoreless.
Freshman guard DeWanna Bonner also scored 14 for the Tigers, who got eight points from freshman Keke Carrier.
Auburn hit 51.7 percent of its shots to take a 33-18 halftime lead to bounce back from an overtime loss to Kent State. AU kept up the hot shooting in the second half, hitting 16-31 field goals in that period.
"I thought we played hard," said Auburn coach Nell Fortner said. "It wasn't always pretty, but they played hard. It is good to rebound from a loss like we did. Everyone contributed and it was a good all-around effort."
Brooke Meunier led Buffalo, now 0-3, with 13 points, but she made just 4-15 field goals.
Auburn will travel to Durham, N.C., to play George Mason on Friday in the opening round of the Duke Classic.