Pavel Buchnevich had a goal and an assist, Brett Howden also scored, and Kaapo Kakko added two assists for the Rangers, who ended a two-game skid and improved to 6-3-1 in their last 10 games. Lundqvist earned his 454th win, tying Curtis Joseph for fifth on the NHL's career list.
Evgeny Kuznetsov scored and Braden Holtby made 27 saves for first-place Washington, which lost in regulation for the second time in four games after an 11-0-2 stretch. The Capitals failed to earn a point for only the fourth time in 24 games, including the second time in 13 on the road.
The Capitals played without right wing Garnet Hathaway and center Nicklas Backstrom. Hathaway was suspended three games earlier in the day for spitting on Anaheim's Erik Gudbranson on Monday night in response to a rabbit punch from Gudbranson, and Backstrom sat out due to an upper body injury.
Panarin made it 2-0 with his second power-play goal of the night on a rebound of Kakko's shot from the left side for his 11th at 3:57 of the third period.
While Panarin's goal was being announced, Buchnevich beat Holtby on the right side off a cross-crease pass from Filip Chytil for his third just 23 seconds later.
Kuznetsov scored from the right circle on a power play to spoil Lundqvist's shutout bid at 7:24. It was his 10th.
Buchnevich found Howden all alone in front, and he beat Holtby on the blocker side for his third with 6 1/2 minutes remaining to restore the Rangers' three-goal lead.
New York's Brendan Lemieux and Washington's Tom Wilson dropped gloves with 3 1/2 minutes to go, after Wilson ran into Lemieux while he was being hit by Alex Ovechkin near the Capitals' bench.
Washington pulled Holtby for an extra skater with more than 3 minutes left but couldn't get anything past Lundqvist.
With the Rangers still on a power play that carried over from the final minute of the first period, Panarin got a pass from Kakko in the left circle and fired it past Holtby's glove side at 1:14 of the second. It extended Panarin's point streak to a career-high 12 games.
After making 10 saves in the first period, Lundqvist had 14 in the second and was helped out by a post for the fourth time when Lars Eller's shot hit iron during Washington's power play about 7 1/2 minutes into the middle period.
Both teams had chances in a scoreless first period. John Carlson and T.J. Oshie both beat Lundqvist but had their shots ring off the crossbar late in the period. Michal Kempny also hit a post earlier.
Panarin has seven goals and 19 points during his streak. He also has eight goals and 12 points in 14 career games against Washington. ... Lundqvist appeared in his 869th regular season game, breaking a tie with Grant Fuhr for 10th on the NHL's career list. ... Rangers C Mika Zibanejad missed his 10th straight game due to an upper body injury. ... Washington LW Carl Hagelin was placed on long-term injured reserve and C Nic Dowd was placed on IR. C Michael Sgarbossa, F Malenstyn and D Tyler Lewington were called up from Hershey of the AHL. ... The Capitals won the first meeting this season, 5-2 at home on Oct. 18. The teams also play March 5 back at Madison Square Garden and March 26 at Washington. ... Referee Furman South was hit in the face by the puck on a clearing attempt by Ovechkin with 9 1/2 minutes left in the first period. South was down on the ice for several minutes and tended to by the Rangers' medical staff. He stayed in the game and received five stitches in the first intermission.
Capitals: Host Vancouver on Saturday to open a three-game homestand.
Rangers: At Ottawa on Friday night.
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Father and son reunited at Rangers game
Army Staff Sgt. Ian Buck returns from a year in Afghanistan to surprise his 10-year-old son, Luke, at the Rangers game.