The Cowboys jumped out to an 8-1 lead behind Matthew's grand slam and RBI hits by Barrus and Wyatt Smith. Grantsville scored all of its eight runs in the 4th inning.
Matthews was supposed to squeeze bunt with the bases loaded, but talked his coach into letting him swing away.
"Coach Anderson wanted me to squeeze, but I told him to give me one pitch," Matthews said. "If I miss it, we'll squeeze. Luckily, I connected."
"I don't know where that came from," said Smith. "He never hits them out of the infield in practice, but thank God it happened today."
Desert Hills, which beat Grantsville 13-8 earlier in the day to force a deciding championship game, cut the lead to 8-7 by scoring five runs in the 4th and one in the 6th, but a crucial 6-4-3 double play ended the Thunder's last threat in the bottom of the 6th.
"This is the 100th year anniversary of this school," said head coach Loren Anderson. "We've been doing things all year, but this is the best."
This is Grantsville's first state baseball title since 2000 and first in 3A.
In the 3A softball championship, Stansbury won back to back titles, beating Uintah in the title game, 8-3.