Zeke Dixson scored 15 points, Bronson King added 13 and the Falcons hit free throws down the stretch to secure the non-league home win.
King had nine rebounds and was 6 for 6 from the foul line, all in the fourth quarter. Prairie was 11 for 14 from the line in the fourth and 18 for 25 for the game.
Prairie’s leading scorer Kam Osborn was held to 12 points, but others stepped up.
“They did a pretty good job early in the game on Kam,” Prairie coach Kyle Brooks said. “But I thought we had pretty good balance from other guys.”
Woodland led 32-30 at halftime. But Prairie (2-4) adjusted its defense and allowed just 17 points in the second half.