Malkin, who had two assists, has 391 goals and 609 assists in 848 games. He is the 88th NHL player, and fifth Russia-born player, to reach 1,000 points.
"Like, finally. Last couple weeks I've been a little bit nervous," Malkin said. "It's like a little bit slow, but it's finally over, 1,000. I (can) breathe normally. Thanking my teammates. Special day for my family, my friends.
"I've played hockey all my life. It's amazing to be here and win here against Washington. A special day for sure."
RELATED: [Malkin reaches 1,000 NHL points | WATCH: All Capitals vs. Penguins highlights]
Sidney Crosby scored twice, Phil Kessel and Jared McCann each had a goal and an assist, and Matt Murray made 38 saves for Pittsburgh (38-23-9), which has won five of six and moved into third place in the Metropolitan Division, two points ahead of the Carolina Hurricanes.
Alex Ovechkin had an assist for his 1,200th NHL point, Jakub Vrana scored twice, and Braden Holtby made 25 saves for Washington (41-22-7), which leads the New York Islanders by two points for first place in the Metropolitan.