The Braves led 15-12 after one quarter, 20-17 at halftime, and 38-35 after three periods, before holding on down the stretch for the tight win.
Eric Wilkie paced Cherokee scoring with 22 points, followed by Zac Smith 15. Nathaniel Morgan led all rebounders for Cherokee with a dozen, and Smith pocketed eight. Wilkie led the Braves in assists with four.
Cherokee sank 25-65 field goals for 38 percent, including 7-19 threes, and a 10-16 effort from the foul line.
OABCIG made 20-50 shots from the field for 40 percent, and converted 6-12 free throws.
A pivotal factor in the outcome was the Braves dominance on the boards with Morgan leading the charge, outrebounding the Falcons 38-24.
The 3-8 Braves host Emmetsburg Friday night in Lakes Conference action.
"This was a real good team win," noted Cherokee coach bob Lee. "We got production from everyone who stepped on the court and worked real well as a team.
"Eric hit some big shots and free throws down the stretch to secure the win. I thought out rebounding was a real key. We really limited their second chance opportunities and gave ourselves a few extra looks on the offensive end."