After being retired in order in both the fourth and fifth innings, Burbank added some drama to the final frame when Davis Anderson knocked a leadoff double into right field.
Lousarian retired the next three batters — all representing the tying run — with a pair of infield popups and a high flyout to right field.
"[L.A. Family] made the plays," Braves Coach Jonathan Malden said. "Our batters who step up every game all year long, they hit the ball.
"[Foothill] just made the catches, so I can't be mad at [our players], they did a good job."
The Braves (18-3), who never lost a game by more than one run all season, struck first on a first-inning double to right field by Bam Rodriquez.
Connor Lockheimer scored on the play, but Lousarian was able to limit the damage to a lone run.
L.A. Family pulled even in the top of the third, when Jack Porras singled to right field with two outs and the bases loaded to score David Aguirre.
The team continued its clutch two-out hitting with a single to right by Morgan Dickerson.
Ryan Keen scored as Dickerson narrowly beat the throw from right field, which skipped away from the first baseman and allowed Lousarian to score from third.
With the Braves flustered, L.A. Family continued to press. It extended the inning for three more batters and scored one more run on a throwing error to take a four-run lead.
Burbank bounced back in the bottom of the third, getting one run back on some heads-up base running by Lockheimer.
With two outs, he doubled, then moved to third and came home on consecutive passed balls to make the score 4-2.
Spencer Malden took the mound for Burbank in the top of the third and shut out L.A. Family on two hits over the final three frames.
But, Lousarian remained sharp until the end, finishing the game in 68 pitches and assuring his team would need no additional runs to fend off the Braves.
"I can't say enough about Tyler," Rick Dickerson said. "To go the whole game at this level is very difficult."
"All season long [my players] have stepped up, and they stepped up again," said Malden of his team, which defeated L.A. Family in the teams' only other meeting this season. "We needed some hits, and they put the bat on the ball, it just didn't happen.
"To get back here and be in the championship game is enough, we're not hanging our heads."