Cagliari were under pressure at a foggy Stadio San Nicola where only a victory would see them promoted.
The first leg ended 1-1 on Thursday as an early goal from Gianluca Lapadula (33) was cancelled out by a late penalty by Bari's Mirco Antenucci (38) and had the second leg also ended in a draw, Bari would have gone up after finishing higher in the table.
Cagliari struggled to create anything for most of the match, but in the pouring rain, Pavoletti volleyed in the winner four minutes into stoppage time.
The result sent Claudio Ranieri's side back into the top flight after a one-year absence. They will join Frosinone and Genoa as promoted sides in Serie A for the 2023-24 season.
Bari finished the season in third, five points ahead of Cagliari in fifth.