Auburn (6-7) trailed by as many as 12 points in the first half before outscoring the Seminoles (8-5) 21-10 down the back end of the first half to cut the Florida State lead to 36-35 by halftime.
Sullivan scored 18 of his 24 points in the first half, keeping the Tigers alive as they battled back from the early deficit. Payne scored nine points in the second half for Auburn as the Tigers overtook the lead.
Florida State's Michael Snaer recorded a double-double in the losing effort, scoring 18 points and pulling down 12 rebounds. Sophomore guard Terry Whisnant added another 16 points for the Seminoles.
The Auburn victory avenged an 85-56 loss to Florida State in Tallahassee last season.
After charging back to cut the lead to one at halftime, Auburn overtook the lead nearly 2 minutes into the second half when a Rob Chubb lay-in put Auburn up 42-40, giving the Tigers their first lead since Auburn was up 8-7 nearly 5 minutes into the game.
Chubb finished with eight points and 10 rebounds for the Tigers. Noel Johnson scored all nine of his points in the second half as Auburn pulled away.
Florida State's Aaron Thomas cut the Auburn lead to seven with 2:58 to play in the game, but the Tigers went 12 of 20 from the free-throw line in the last 2:01 of the game to seal the win.
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Former Kentucky guard Ed Davender, the only Wildcat with at least 1,500 points and 400 assists, has died. He was 49.
Guard Naz Mitrou-Long, whose 2015-16 season ended in December due to hip problems, has been granted a hardship waiver for the coming season, Iowa State said.
As the Sooners look to life without superstar Buddy Hield and his sidekicks, it's clear their unseasoned players will need to grow up fast.