Austin Zirk finished with 16 points for the Mountain Lions.
While Tucker County blistered the nets in the first half, Greater Beckley struggled from the field in connecting on just 39.3 percent of its shots, which included a 0-of-8 effort from behind the arc before the half.
Gutshall believes that his team's vast tournament experience helped, especially early in the game.
"We've shot here and these kids have been here all four years of their careers and all of them have played on the Civic Center floor, which does make a difference," Gutshall said. "Our kids were relaxed and I think we play a little tougher defense that a lot of people are used to.
"Our kids play tough, I've got to give them credit."
Greater Beckley rallied in the second half, cutting Tucker's lead to just five midway through the third quarter, but could get no closer than six points in the final quarter.
Javonne Staunton-Bailey led Greater Beckley with 17 points, followed by Elisha Kidd with 14 points and Keith Mullins with 11 points and 10 rebounds.
"We gave up a lot of threes in the first two quarters and we addressed that at halftime," said Burd, whose team hit just one 3-pointer in the second half. "I thought we came out, we battled and I thought our guys didn't give up.
"We played great defense in the second half. We didn't give up the threes we gave up in the first half, it just came down to we just couldn't cut into the lead."