Jagr beat Oilers goalie Devan Dubnyk 1:46 into overtime with a high wrist shot for his third goal of the season.
Ales Hemsky and Justin Schultz scored in response for the Oilers, who were without three of their top four centres — Ryan Nugent-Hopkins (day-to-day with a shoulder injury), Shawn Horcoff (broken knuckle) and Eric Belanger (broken toes).
Adding to their woes, centre Anton Lander left the game in the first period with a foot injury.
The Oilers (4-3-3) are now winless in their last four games.
There were few good chances in a rather sedate first period, most of them belong to the Stars while they were short handed. Dallas had several odd-man rushes late in the first and almost converted on one of them as Cody Eakin had Dubnyk beat but rang his shot off the post.
Edmonton broke the scoreless deadlock three minutes into the second following a mad scramble in front of the Dallas net. Nail Yakupov rang a shot off the post behind Stars starter Kari Lehtonen before Hemsky banked the rebound in off a defender.
Sam Gagner had an assist to extend his point streak to 10 games.
The sound of metal clanging rang out through Rexall Place with seven minutes left as Loui Eriksson hit the post behind Dubnyk, leading immediately to a rush by Yakupov, who also hit the post on his shot.
A minute later the Stars tied the game as a shot by Benn appeared to deflect off Oiler Jeff Petry and into the Edmonton net. It was Benn's third goal in six games since ending his free agent holdout.
Dallas went up 2-1 with 1:16 left to play in the second period as Roy blasted a shot from the point during a power play that found the back of the net untouched. It was Roy’s first goal as a Star.
Edmonton tied the game 2-2 eight minutes into the third on a power play of their own as Schultz let loose a rocket from the point past Lehtonen. It was the third goal of the season for the Oilers rookie defenceman.
The Stars return home to take on the Ducks on Friday. The Oilers start a quick two-game road trip on Saturday in Detroit.
Notes — It was the first of three meetings between the two teams this season. The Star captured all four meetings last season by a combined 14-4 margin, holding the Oilers to a one goal in each game… Stars D Alex Goligoski was a surprise healthy scratch. Goligoski is the Stars’ highest paid defenceman with a $4.2 million price tag and is second on the overall team payroll behind Benn… With the three injured centres, Oklahoma City call-up Marc Arcobello made his NHL debut playing on the Oilers top line between Taylor Hall and Jordan Eberle. … The latest injuries added to an already long list of hobbled players for Edmonton that includes Andy Sutton (knee), Ryan Jones (eye), Ben Eager (concussion) Mark Fistric (back) and Theo Peckham (hip)… Stars F Ray Whitney is out with a broken foot… The Stars came into the game having been short handed a league-high 50 times this year.