The Taipans fifth straight win lifts Cairns to third while the Breakers are sixth, outside the top four playoff spots.
The Snakes' have a 12-9 record and are now in line for their first playoff action since the 2016/17 season.
The Breakers led 78-71 with half a quarter to play, but Cairns fought back to close out the game on a 14-1 scoring run.
Taipans coach Mike Kelly said this scalp was massive in terms of their playoff push.