Jagr took a pass from Shanahan and ripped a shot over the net, a rare miss for the newest members of the 600-goal club.
"That was funny," Jagr said. "Shanny told me, 'Good dump.'"
The Czech star scored twice during another milestone night and Henrik Lundqvist made 34 saves in his third career shutout.
Just two nights after Jagr became the 16th NHL player to score 600 goals, he passed Jari Kurri and set the record for goals by a European-born player.
"It's huge," Jagr said. "Jari Kurri was a guy everybody looked up to from Europe. He was our idol."
Shanahan, who reached 600 earlier this season, and Marcel Hossa also scored.
It was the first time since Detroit's Brett Hull and Steve Yzerman on March 21, 2004, that 600-goal scoring teammates connected in the same game, according to the Elias Sports Bureau.
Lundqvist has picked up his game and was sharp throughout, making 23 saves in the first two periods and protecting a lead all night. During the middle frame, he turned away Mike Commodore after defenseman Karel Rachunek turned over the puck in front, and then rushed across the crease to deny Ray Whitney's one-timed shot at the left post.
After allowing at least four goals in six of his first 10 outings, Lundqvist has yielded a total of 14 in his past seven starts.
"I always keep telling myself to concentrate on the next puck," Lundqvist said following the Rangers' first shutout this season. "It sounds silly ... but it keeps me on my toes."
Jagr maneuvered in the left circle and ripped a shot in with 6:24 left in the second period to make it 3-0, then closed the scoring by tipping in Aaron Ward's drive in the final frame.
New York killed off a 5-on-3 power play that started in the first minute of the second period and ended with the Rangers having an advantage.
After a lackluster loss in Pittsburgh last Saturday night, that angered coach Tom Renney, the Rangers have bounced back with two of their best efforts of the season against the last two Stanley Cup champions.
"It's big for us," said Matt Cullen, a member of the Hurricanes last season. "We feel like we're starting to find our game and kind of buying into the way that we need to play in order to win.
"We beat two really good teams and we did it by playing the right way."
New York, only 5-4-1 at Madison Square Garden, followed up a 4-1 home win over Tampa Bay on Sunday by thoroughly outworking Carolina.
That doesn't bode well for the Hurricanes, who started a three-game-in-four-day road trip -- that includes a Friday matinee in Boston -- with an uninspired performance of their own. Carolina's three-game winning streak was snapped.
"I thought we played a lazy game," Hurricanes coach Peter Laviolette said. "They had a step on us in the skating and the battles."
The Rangers turned the heat up early on goalie Cam Ward and the rest of the Hurricanes. Less than a minute after Martin Straka nearly converted a Carolina turnover into a goal, Hossa scored his first of the season at 3:39.
New York didn't ease up and turned hard work down low into another tally.
Cullen tried to stuff a shot in from behind but was denied. Straka gathered the puck and brought it back behind the goal before finding Shanahan in front. Shanahan knocked it past Ward for his 17th of the season and 615th overall.
The 37-year-old Shanahan is on an eight-game point streak (five goals, five assists) and has a goal in three consecutive games and four of five.
- The teams completed a trade before the game as the Rangers acquired veteran forward Brad Isbister from Carolina for C Jakub Petruzalek and a conditional 2008 draft pick. Isbister, in the AHL all season, will report to the Rangers' Hartford affiliate.
- Jagr has 30 goals against the Carolina franchise in 63 games.
- Rangers RW Jed Ortmeyer was cleared to practice without contact. He has been out all season due to a pulmonary embolism.
- The Hurricanes are 12-5-2 after an 0-3-1 start.