Woods responded with a 3-pointer from the right wing as time expired to force overtime and help Monett (1-3) earn a 51-46 victory on Dec. 7.
"Kyle is a great player," said Monett coach Ty Goetz. "Sometimes he struggles to stay under control, but he has the ability to go hit a big shot when we need it."
Aaron Patton hit a free throw with 1:15 to pull the Cubs within five.
Woods hit a driving layup with 46 seconds to help Monett inch closer.
With 18 seconds left, Monett's pressure defense forced the Mustangs (1-1) to throw the ball away to set up Woods' shot.
The Cubs' defense forced three McDonald County turnovers in the final 46 seconds and held the Mustangs without a field goal over the last 3:48 of regulation.
The Cubs carried the momentum into the extra four minutes of overtime as seniors Caleb Blue and Woods staked Monett to its first lead since the third period with back-to-back buckets.
Monett outscored the Mustangs 7-2 in the extra frame to secure victory.
The Cubs started the game red-hot leading 14-4 after one quarter of play.
McDonald County battled back in the next two periods, and outscored the Cubs 32-22.
"We will always take a win," said Goetz. "I don't care how we do it. I like the way we started the game. We need to play with that kind of effort every day."
Scoring for McDonald County: Drew Fickle, 16 points; Josh Serr, 9; Tyler Sherwood, 8; Pablo Alvarez, 6; Jake Wood, 4; and Tyrell Lett, 3.
Scoring for Monett: Woods, 23 points; Arron Patton, 9: Zach Hammond and Blue, 6 apiece; Sean Rosebaugh, 4; Chad Swanson, 2; and Elijah George, 1.
Monett will be at home on Dec. 14 against Hollister.