Sek Henry had 20 points and eight assists, while Brandon Ashley (14 points, nine rebounds), Tom Abercrombie (12 points) and Finn Delany (10 points) all reached double figures.
Discipline also let Adelaide down, sending the Breakers to the free-throw line on 42 occasions.
It was a gripping encounter throughout, with just one point separating the sides at the end of each quarter. The Breakers led 21-20 after the first quarter before the 36ers took a 45-44 lead into the main break.
When the Breakers took a 70-69 lead into the final quarter, the game seemed destined to be decided by a crucial play in the final minute but after some recent drama-filled endings, the Breakers closed out the victory down the stretch.
The win sees the Breakers leapfrog the 36ers into sixth on the table, with both teams now sitting on 8-10.
It's been an impressive turnaround for Dan Shamir's team considering they let Corey Webster leave to join the Zhejiang Guangsha Lions in China on December 18, which seemed a signal they had given up on the 2019-20 season. The Breakers haven't lost since. They've also been without RJ Hampton, the young talent expected to be picked up in the first round of the NBA draft, after he suffered a hip injury.
The Breakers' road trips continue in the New Year with back-to-back games against South East Melbourne and Cairns before they finally return to Spark Arena on January 12.