Chad Pedigo scored a career-high 27 points and hit big shots in the fourth quarter as the host Chieftains edged the Titans.
Pedigo scored 16 of his 27 points after halftime, and put River ahead to stay with a free-throw line jump shot with about three minutes remaining.
Nathan Hawthorne sealed the win with a pair of late free throws that came after he missed a pair of foul shots then made a steal and was fouled. River then fouled to prevent Union attempting a tying 3-pointer.
Riley Hawken scored 25 points for Union.
A big third quarter had the Chieftains up by as many as eight early in the fourth period. But the Titans rallied and held a four-point lead.