Jagr reached the mark by setting up power-play goals by Michal Rozsival in the first and third periods. The Rangers captain added a third assist with 13:51 left, sending a centring pass that Martin Straka fired past Olie Kolzig to provide New York with a two-goal cushion.
Straka added an empty-netter with 29.5 seconds remaining.
Alex Ovechkin and Chris Clark scored power-play goals for the Capitals, who were 0-for-15 with the extra man in their last four games. Coach Glen Hanlon reconfigured the unit on Friday, and the change produced the desired results.
But the Rangers limited Washington to only 19 shots, and Henrik Lundqvist stopped all but two in a sufficient encore to his 5-0 shutout of Tampa Bay on Friday night.
Jagr has 612 goals and 889 assists in 1,165 career games. But he failed to fulfil high expectations in Washington before being traded to New York in 2004, and thus many in the sellout crowd booed him every time he touched the puck.
Rozsival put the Rangers up 3-2 with 15:43 to go, beating Kolzig on a blast between the circles off a centring pass from Michael Nylander. Jagr got the puck to Nylander, who was behind the net.
Two minutes earlier, Clark took a pass from Alexander Semin and deked Lundqvist before scoring on a backhander.
The Rangers went up 2-1 midway through the second period when Marcel Hossa slammed in the rebound of a shot by Brendan Shanahan with New York on the power play. After scoring two goals in his first 50 games this season, Hossa has three in the last four.
Rozsival gave New York a 1-0 lead at 11:18 of the first period. The score came after the Rangers' Ryan Hollweg and Washington's Brian Sutherby fought; Sutherby got an extra two minutes for charging.
Ovechkin tied it at 18:20 of the period. After Lundqvist chased down the puck behind the net and cleared it, the goaltender couldn't set up in time to stop Ovechkin's shot from the right side.
New York outshot Washington 11-1 in the opening 12 minutes and 16-6 in the first period.
Notes: New York won the season series 3-1. ... Former Orioles infielder Cal Ripken, who was elected into the Baseball Hall of Fame last month, received a standing ovation when introduced to the crowd during the second period. He watched the game in the owner's box with Ted Leonsis. ... New York LW Pascal Dupius, acquired Friday in a trade with Minnesota, was scratched. ... Ovechkin has four goals and four assists in eight career games against New York. ... Hossa, who assisted on Straka's empty-net goal, has 10 points this season - five in five games.