Pierce, who scored 28 points in his team's 105-102 overtime victory over the Milwaukee Bucks, has spent all of his 13 seasons in the NBA with the Celtics. Hall of Fame players Larry Bird and John Havlicek, who both also achieved the mark, spent their entire careers with Boston.
"It was really emotional," Pierce told television reporters after he passed the mark from the free throw line and received an ovation from his home crowd.
"I've been through so many hard years here. To come so far at this point in my career I'm just blessed and happy to still be a Celtic."
Pierce now has 20,005 points and joins three of his current team mates, center Shaquille O'Neal, power forward Kevin Garnett and guard Ray Allen in achieving the milestone.