A steal and a score by Clements with 28 seconds to play in the third quarter pushed Monroe's lead to 42-36.
Breanna Glover scored the first four points of the fourth quarter to cut Glasgow's deficit to two points, 42-40, with 5:30 left in the game. That was as close as the Lady Scotties got to coming back and winning the game.
Clements responded with a field goal 25 seconds later, then Molly Harlin nailed a 3-pointer with 4:33 to play in the game to give Monroe a 47-40 advantage.
Glasgow got to within four points with 1:24 to play on a basket by Smith, but the Lady Falcons secured the win by making free throws over the last minute.
“We were trying a little bit of everything to slow (Clements) down,” Stinson said. “We let her get the ball too deep in the paint and she is going to make those shots.”
After Clements' 34 points for Monroe, Kayla Murray added nine, while Harlin scored seven, Lauren Turner posted six points and Kelsey Kirkpatrick finished with a point.
Kelsey Greer led Glasgow with 18 points, while Smith scored 14, Glover posted 13 points and Emily Alexander finished with four.
The Lady Falcons are in the Touchstone Energy All “A” Classic State Tournament for the third consecutive year. They open against Magoffin County at 8:30 p.m. Central on Wednesday.