The entire Bruins team came off the bench to celebrate with Bergeron after the goal was scored.
"It's a special moment and it doesn't happen often," Marchand said. "Obviously, it couldn't be with a better guy. It's another milestone in such an incredible career."
Bergeron is the fourth Bruins player to have 1,000 points, joining Ray Bourque (1,506), Johnny Bucyk (1,339) and Phil Esposito (1,012).
"If he had any kind of cheat in his game he might have 1,200 or 1,300 points," Boston coach Jim Montgomery said. "But he's just so dedicated to playing the game the right way and helping the team have success. He always thinks team, it's amazing."
David Krejci had a goal and an assist for the Bruins (17-2-0), who have won seven straight. Linus Ullmark made 32 saves.