Muller's entrance from the bench gave him 710 appearances for Bayern, overtaking the record set by keeper Sepp Maier who retired in 1979, and his 150th Bundesliga goal sealed a 2-0 victory.
In a strange twist of fate, back in 2008 Kompany was making his last club appearance as a player in Germany in the very game where Muller made his debut, before Bayern's current manager left Hamburg to join Manchester City.
"Outstanding. I witnessed his first game. I was there with Hamburg on this pitch. 710 games later, it's unbelievable," Kompany said.
"He gave 100% in 710 games, but not only in the games, but also in training. That's what makes Thomas so special.
"There are a few more games that he can still play and we are definitely pleased that he's got a few more in his locker and the fact that he can keep going like this, it's so important for us."
Kompany said his side's performance dipped after the break, but luckily he has players like Muller he can call upon when the need arises.
"Very positive first half, and then in the second half we were just one step later than Freiburg on second balls, and we lost a little bit of the momentum," he said.
"But then I have to say that we're very fortunate to have very good players that can come on and make the difference, and Thomas Muller came on, Kingsley Coman too, and the players from the bench were very important for us to win this game.
"Positives and things to learn and we also got to celebrate a fantastic moment for Thomas Muller and that was important as well for us today."
