The Cubs (3-8, 1-0) entered the contest knowing that they had a huge test in the Mountaineers.
"We knew coming in that Mt. Vernon was a tough squad," said Monett coach Ty Goetz. "Our game plan was to slow the game down on offense and get quality possessions. We couldn't execute that plan for all four quarters tonight."
Woods hit a short jumper as time expired to tie the score at 8-8 to end the first period.
Woods, who led all scorers with 25 points, scored all 8 points for the Cubs in the frame.
The second quarter proved more difficult for the purple and gold. Mt. Vernon (10-4, 1-0) cut off Monett's dribble penetration that worked earlier in the contest and countered with a 15-2 run to open the period.
Mt. Vernon took a 30-15 lead into the locker room.
An 8-0 run to open the third period, by the green and white, erased any hope for a Monett comeback. Mt. Vernon led 46-25 to start the final period.
"We need to focus on executing for the entire length of the game," said Goetz. "We will move on and prepare for our next game."
Scoring for Mt. Vernon: Chandler Meyers, 17 points; Shane Williams and Zane Phillips, 14 apiece; Grayson Ketron, 8; Luke Call, 6; and Skylar Phillips and Joey Curl, 3 each.
Scoring for Monett: Woods, 25; points; Caleb Blue, 4; Sean Rosebaugh, 3; Zach Hammond, Elijah George and Quincy Jackson, 2 points each; and Aaron Patton, 1.
The Monett Lady Cubs dug an early hole and could not recover falling 37-31 to Diamond on Jan. 3.
Monett trailed 13-8 after one period and 17-13 at halftime.
The Lady Wildcats outscored the Lady Cubs 13-6 in the third period to lead 30-19.
The purple and gold made a valiant effort to fight back in the fourth quarter using an 8-0 push to cut the Diamond lead to three (30-27) with 4:30 left in the game.
However, it wouldn't be enough as the Lady Wildcats held Monett to 1 point over the remainder of the game.
Scoring for Monett: Haylee Morris, 15 points; Faith Schmidt, 7; Brooke McLean, 4; Cheryl Barnes and Kelsey Wiseman, 2 each; and Jessica Harper, 1.
Monett hosts Morrisville and the Lady Cubs travel to Carl Junction tonight. Both contest are set to tipoff at 7 p.m.