Jacob Hjort scored 28 points, including a game-winning 3-pointer with four seconds left.
Hjort made four 3-pointers in the fourth quarter. Eleven of the Chieftains 19 field goals were from behind the arc.
The Chieftains struck back after the third quarter in which they were held to six points.
River won despite missing its starting post Spencer Black, who likely won’t be available for another week due to injury.
“We had some young kids pick up the slack,” Chieftains coach David Long said. “Everyone played solid.”