Muir (5-4, 3-3 in league), ranked sixth in the CIF Southern Section Southeast Division, countered with a 39-yard field goal by Jorge Castro.
But Burbank engineered a seven-play drive that covered 80 yards in under two minutes, capped by Castro's 22-yard run to push the Bulldogs (4-5, 3-3) ahead for good.
"That was a phenomenal game," Burbank Coach Hector Valencia said. "We needed this win, obviously. Every game that we play is a playoff game; we have to win. We lose a game and we're out. At least now we're still in the running.
"We had a chance to control our destiny tonight and our kids demonstrated a lot of character."
The loss for Muir snapped a three-game winning streak heading into its season finale next week against Pasadena at the Rose Bowl.
"We didn't get the stops when we needed them — bottom line," Mustangs interim coach Dave Mitchell said. "We didn't make tackles. Kids knew what was coming and we missed some assignments. But we just need to make tackles when it's time to make them. That last touchdown [by Castro] — no way that should have happened. We need to make tackles fourth-and-long like that."
Castro also had a sack on Muir freshman quarterback Darick Holmes on the second-to-last play of the game.
On a third-and-15 from Muir's own 25, Castro dropped Holmes for a loss of five yards. Holmes completed a pass on a fourth down for 10 yards, but it came up 10 yards short and Burbank milked the clock.
"Herman's been doing a lot of things for us all year," Valencia said.
Muir, which is tied for fifth place in league with Burbank, was led by Holmes' three touchdowns.
He completed seven of nine passes for 168 yards and two scores. He also tallied 78 rushing yards on nine carries and scored on a 14-yard run.
Kevon Seymour had four receptions for 122 yards and two touchdowns for 84 and 25 yards.
Tarien Owens scored the game's opening touchdown for Muir on a 50-yard punt return.