Blair Betts and Petr Prucha also scored for the Rangers and Kevin Weekes made 30 saves in his second start of the season. Weekes surrendered seven goals on 32 shots in his first start, losing to Buffalo 7-4 on Oct. 14.
Chris Pronger and Ryan Getzlaf scored unassisted goals 83 seconds apart in the second period for Anaheim and Teemu Selanne ended a 10-game goal drought.
Anaheim (9-0-4) is one of two teams that has yet to lose in regulation, along with Buffalo (10-0-1). By earning a point in the standings for the 13th straight game, the Ducks broke the previous club record set during the 1996-97 season. They are the first team to record at least one point in the first 13 games of a season since the 1994-95 Pittsburgh Penguins.
Jagr scored his fourth goal of the season and 595th of his career moments after Anaheim defenceman Francois Beauchemin got a roughing penalty for punching Aaron Ward in the face in front of the Rangers' net. Jagr beat Jean-Sebastien Giguere high to the glove side with a one-timer from the right circle after defenceman Michal Rozsival faked a long slap shot and fed it to the Rangers' captain.
It was the 103rd winner of Jagr's career, tying Shanahan for fourth on the career list behind Gordie Howe (121), Phil Esposito (118) and Brett Hull (110).
The Ducks, who had only five shots on net in the second period, capitalized on two sloppy turnovers by defenceman Marek Malik deep in the Rangers' end to grab a 3-2 lead at 12:59 of the period.
Pronger intercepted Malik's attempted clearing pass, moved in a couple of strides and beat Weekes with a 35-foot wrist shot that tied it. Getzlaf scored moments later with a one-timer from 45 feet after Malik kicked the puck away from Shawn Thornton in the right corner and right onto Getzlaf's stick.
But New York pulled even with 15:13 left in regulation, as Prucha converted a rebound after Matt Cullen tried to stuff it past Giguere in the crease.
The Rangers, 0-for-9 on the power play in Monday's 4-1 loss to the Los Angeles Kings, took a 2-1 lead while Anaheim's Andy McDonald was serving a tripping penalty. Michael Nylander's wide shot caromed off the end boards and Jagr nudged the puck into the crease before Shanahan backhanded it into the net.
The goal was Shanahan's 11th this season and 609th of his career, surpassing Dino Ciccarelli for 13th place on the career list and putting him within one of Bobby Hull's total.
Notes: This is the eighth time the Rangers have played back-to-back games in Anaheim and Los Angeles, and the first time since Dec. 14-15, 2000. They have never swept both games. ... It was the first meeting between the teams since Oct. 28, 2003, at Madison Square Garden, when backup goalie Martin Gerber led the Ducks to a 3-1 victory with 38 saves. The Rangers' had not played in Anaheim since Feb. 21, 2003, when they got two goals each from Pavel Bure and Bobby Holik in a 6-2 win.