"We miss playing at home," said Mustangs player Emoni Jackson, citing fan support.
The sophomore finished with 16 points and 15 rebounds.
A Jackson bucket gave Muir (14-3, 3-0 in league) a 35-30 lead with a little under two minutes remaining. A basket from Bulldogs' Aja Locke and a pair of foul shots by Damarie Gonzalez cut the deficit to 35-34.
But it was Muir's Jerrica Daniels, who had limped off the court early in the third period with a tweaked ankle, who sealed the game with two free throws.
Early on, Burbank (9-8, 2-2) had trouble adjusting to Muir's defensive press. But the Bulldogs got their passing in order, and the Mustangs held just a 19-16 lead at half time.
"We work on it, and we worked on their half-court trap," said Burbank Coach Bruce Breeden. "They took it off because we were beating it. Turnovers killed us."
Muir ultimately switched to a zone for much of the third quarter, before reinstating the trap late.
"It seemed like we got a little tired, and they started breaking it," said Muir Coach Gary Johnson. "They've got a smart coach there, so he knows how to break it. It became cat and mouse."
Muir came out strong in the second quarter, but Burbank rallied to take a 16-13 lead. The Mustangs regained the advantage heading into halftime, and never relinquished the lead.
"We just have to execute more," Jackson said. "They were playing very aggressive. We have to be stronger with the ball and make smarter passes. Once they get use to our press and they adjust to it, we have to adjust to our defense."
Locke led the Bulldogs with 12 points and five rebounds.
"Our game plan [was to] play tight and limit them to one shot, which we didn't get done," Breeden said. "Everything else, picture perfect."
Tahniya Sweatt added 13 points and nine rebounds for Muir.