With a basket in the third quarter, Woods scored his ninth point of the game and the 1,286th of his Monett career to become the Cubs' all-time leading scored.
"Kyle is a special player," said Monett coach Ty Goetz. "He has been a four-year starter, and watching him develop as a player has been a honor."
The Cubs (4-8) started the game without intensity and effort.
Marion C. Early led 7-6 after the first period and 17-14 at halftime.
"I wasn't pleased at all with the way we started the game," said Goetz. "I told the boys at halftime time that the problem wasn't with the X's and O's but with our effort."
The Cubs listened too their coach and woke up in the third period. Monett outscored the visitors 15-5 in the frame.
"In the second half we moved the ball really well," said Goetz. "We played liked we had something to prove. I was proud how the boys responded."
The Cubs also won the fourth quarter by a 20-13 margin.
Scoring for Marion C. Early: Dustin Hargus, 14 points; Rylan Hill, 10; Josh Devine, 7; and Brevin Hill and Darian Potts, 2 apiece.
Scoring for Monett: Kyle Woods, 18 points; Aaron Patton, 13; Elijah George, 5; Sean Rosebaugh and Quincy Jackson, 4 each; Zach Hammond, 3; and Caleb Blue, 2.
Monett hosts Aurora on Jan. 11. Tipoff is set for 6 p.m.