Jagr, the NHL's active leader in goals, assists and points, had a hand in all four goals for Dallas. Ray Whitney, Phoenix's leading scorer last season, scored a goal in the first game against his former team.
Loui Eriksson broke a 3-all tie when he took a pass from Jagr in the slot and beat Mike Smith. The sequence started with a turnover by Phoenix's Martin Hanzal, and Jagr grabbed the rebound in the corner after a hard shot by Derek Roy.
Radim Vrbata scored twice for the Coyotes, who went to the Western Conference finals last year after the franchise had never won more than one playoff series in a history dating to 1979 in Winnipeg.
Whitney gave Dallas a 3-2 lead early in the third period with a power-play goal on a feed from Jagr. The Coyotes answered quickly with Vrbata's second goal on a breakaway after Jordie Benn gave away the puck at centre ice.
The Stars spent 10 of the first 15 minutes of the second period killing penalties and it cost them a 1-0 lead.
Dallas killed a four-minute power play after a high stick by Philip Larsen drew blood from David Moss and led to a brief delay for a cleanup on the ice. The Stars couldn't get through a regular two-minute penalty a short time later. Matthew Lombardi's pass across the ice to Vrbata drew Kari Lehtonen's attention, and Vrbata flipped the puck to Lauri Korpikoski for an easy shot into an open net.
The Coyotes went ahead 2-1 after Brenden Morrow was called for high sticking. Vrbata drove a shot with Hanzal shielding Lehtonen, and the puck bounced over the goalie and into the net. Hanzal originally got credit for the goal before a scoring change.
Jagr tied it at 2 late in the second with his second goal and the 667th of his career when a shot by Stephane Robidas was blocked, but Jagr found the puck first in the slot and shot it past Smith.
Jagr scored the first Dallas goal of the season late in the first period after a pass from Eriksson left him alone with the puck in front of Smith. The goal was one of the few smooth plays in an otherwise rough opening period that showed signs of the long layoff and short training camp.
Stars newcomer Derek Roy badly misplayed a puck at one blue line and fell down at the other, a sequence that eventually led to Vrbata having a clean shot that Lehtonen stuffed from close range.
Jagr had another good scoring chance from the same spot before his first-period goal, but didn't get enough of the puck. That was the only good opportunity on the first power play of the season for Dallas, which was the worst team in the league with the extra man last season.
NOTES: Coyotes winger Raffi Torres missed the opener as the first of eight games remaining from a suspension imposed during last season's playoffs. Torres originally was suspended 25 games for a hit on Chicago's Marian Hossa in the first round. The suspension was later reduced to 21 games. ... Texas Rangers left-hander Derek Holland, a self-professed hockey nut and vocal fan of all Dallas-Fort Worth pro teams, attended the opener in a Jagr No. 68 Dallas jersey.