Vincent Kompany's side took the lead through Dayot Upamecano in the first half, but Stuttgart responded after the break to briefly put Bayern under pressure.
Josha Vagnoman scored the equaliser in the 52nd minute after Manuel Neuer had made an important save from Tiago Tomas.
However, Bayern quickly regained control and showed the attacking quality that made them champions last season.
Michael Olise restored Bayern's lead after being played through by Joshua Kimmich, before Vagnoman's own goal gave the home side further breathing space.
Summer signing Ismael Saibari then made an immediate impact after coming off the bench. The Moroccan set up Pavlovic for Bayern's fourth goal before creating another chance for Luis Diaz, who completed the scoring.
Pavlovic was delighted with Bayern's response after Stuttgart's equaliser and said the champions' persistence eventually wore down their opponents.
"We gave everything from start to finish," Pavlovic said.
"Against Stuttgart, they often fade a bit in the second half and don't have as much energy left. That was the case again today."
Bayern continued to push forward after going back in front and scored three more times as Stuttgart struggled to contain the champions.
"We kept going, didn't give up, and scored our goals," Pavlovic added.
"Of course, it's a fantastic feeling to be able to celebrate with the fans again after such a long time."
The 22-year-old midfielder was also pleased to get his name on the scoresheet after Saibari's unselfish pass left him with a simple finish.
"For my goal, I was running alongside the defence, Ismael Saibari saw me and made a great assist," Pavlovic said.
"I'm very happy about my goal."
Pavlovic has become an increasingly important player for Bayern since breaking into the first team in 2023. He made 49 appearances in all competitions last season as Kompany's side won the Bundesliga title.
His goal against Stuttgart was his first since April, when he scored in Bayern's 4-3 victory over Real Madrid.
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