With the win, the Blue Devils remain undefeated in four games, with each being a region contest.
Sophomore running back Hunter Woodall picked up 134 of Falkville's 165 rushing yards, carrying the ball 28 times while scoring one touchdown.
"This was a great game for us. It was definitely a great game," said Woodall, whose team is 4-0 with all four victories coming in Class 1A, Region 6 play.
"For me, the holes were there when I got the ball. Our line did a great job just like they have been doing all season. And everyone can see that we've stepped it up on defense. We're all excited right now but we'll have to get back to work soon so we can keep on keeping on."
The Blue Devils' defense kept Meek in check for most of the game. The Tigers managed 157 yards of total offense, 101 of which came through the air. Falkville intercepted three Meek passes, and its defense forced a safety.
Neither team managed any first quarter points.
With 1:55 left before intermission, Falkville quarterback Aaron Estes connected with Lucas Johnson for a 12-yard touchdown pass. Ryan Sullivan kicked the extra point. Meek scored a touchdown when Seth Hayes found Jentson Hiller on a 30-yard scoring pass. The extra point attempt failed and Falkville led 7-6 at the half.
Late in the third quarter, Meek's Seth Newton was tackled in his end zone for a safety. With 1:57 left in the third period, Woodall scored on a 5-yard run for Falkville.
"This was a great win for us," said Falkville coach Joel Schrenk. "It was lights out with our defensive playing like it did."