Cade Harvey tallied 22 game-high points to lead the winning Hawks, while Blake Simons added 16.
Eric Wilkie paced Cherokee with 13 points, followed by Stetson Dagel 10, and Nathaniel Morgan eight. Dagel also led the Braves in rebounds with six.
HMS inched out to a 21-20 halftime lead and held a 38-34 bulge heading into the final period.
Cherokee sank 18-53 field goals for 34 percent, including just 1-10 three-balls, and cashed in 10-14 free throws.
HMS made 20-55 shots for 36 percent, and netted 10-18 free throws.
"We did a nice job of taking care of the ball tonight (only committed five turnovers), but struggled a little putting the ball in the hole," said Cherokee coach Bob Lee.
"We thought our guys played hard tonight, and put themselves into a position to have a chance to win late in the game. Unfortunately, we missed a couple shots down the stretch and HMS did not."
The 0-12 Braves trek to Emmetsburg Friday night to resume Lakes Conference action.