Auburn (8-3) jumped out to a 38-27 lead by halftime. In the second half, Chris Denson exploded for the Tigers, scoring 17 of his 19 points in the final frame.
Auburn outscored the Rattlers 43-23 in the second half to pull away. Denson boosted the Tigers' effort late, after having sat for most of the first half in foul trouble.
"I think our guys are starting to get what our identity has got to be," Auburn head coach Tony Barbee said. "We've got to play harder and tougher than every team we played against, every night out. We did that tonight."
While the Rattlers entered Saturday night's game with just four wins on the year, their worst defeat of the season came by just a 17-point margin, in a 67-50 loss to Princeton on Nov. 10. Saturday, the Tigers beat Florida A&M by 31 points.
"Florida A&M is a team that's -- their record is not indicative of how good they are or how hard they play," Barbee said. "They play really, really hard. No team has beat them like we beat them. Nobody has outrebounded them the way we did, and nobody has held them to the shooting percentage that we did.
"I thought, from start to finish, we played harder and tougher than them."
Payne's double-double was his first of the season, and the second of his career.
"Allen Payne was a monster out there," Barbee said. "He was on it defensively; he was on it offensively, on the offensive glass. Early on he got us two or three offensive rebounds in a row to set the tone.
"On top of it he has not only the 16 points and 13 rebounds, but five assists and no turns. That's what seniors are supposed to do."
Payne had his double-double recorded by halftime, entering the break with 12 points and 11 boards.
"I just wanted to be more aggressive," Payne said. "We all heard Coach say that he's looking for more guys to step up and produce, and with me playing nearly 30 minutes a game, I definitely took on that challenge. I had a good week of practice leading up to this one, and it carried over."
While Payne came out strong early, Denson started the game sloppy, picking up two fouls just 3:31 into the contest. Denson did not return until the second half.
When he finally made it back on the floor, the senior guard responded.
"He was one of those guys that I didn't think was ready to play right from the beginning," Barbee said. "That shows with him getting two quick fouls. When you're not ready to play, that's what happened. I challenged him a little bit at halftime, and he responded."
The Tigers will kick off Southeastern Conference play when they return to action against Ole Miss on the road Thursday. Florida A&M will host North Carolina-Central on Jan. 11.