Chester Jets won 96-94 at Newcastle Eagles to send the BBL title race into the last weekend and give themselves the edge over their rivals. Jets' Trey Moore led all scorers with 33 points, while Sullivan's 22 points led the way for the Eagles.
The Jets, needing to win by nine points, posted a 20-2 run in the third quarter to lead by 18 points.
But in the last quarter, future England cap Andrew Sullivan sparked a 17-6 Eagles run for a thrilling finale.
Moore scored nine points of Chester's third-quarter streak which had the Eagles facing losing the title at home.
Thanks to Sullivan, and late three-pointers from Charles Smith and Jeremy Hyatt, Eagles can still win the title if they beat Sheffield on Sunday.
But if Chester win against London Towers on the same day, the Jets would win the title on points difference.
Elsewhere, Milton Keynes made sure of the final playoffs spot with a 78-62 win over the Leicester Riders.