Republic jumped out to a 19-10 lead in the first period and cruised into halftime with a 41-19 advantage.
Kyle Woods led Monett in scoring with 11 points. Tyler Webb added 10 points. Tyler Green added 8 points. Jacob Fair tallied 7 points, and Travis Thompson and Jarred Witt contributed 3 points each.
"Republic was the more physical team tonight," said Monett coach Ty Goetz. "I thought a key to our three-game winning streak was the fact we outrebounded our opponents. Tonight, Republic owned the boards and earned the win."
Monett hosts Reeds Spring on Tuesday night. Tipoff is set for 6 p.m.