"We got two pretty lucky goals today, just amazing bounces," Lehtonen said of his team's first two goals. "[Oilers goalie Devan] Dubnyk was playing great. He had a shutout going on in my mind until the last two goals.
"He had no business having those first two go in on him."
The Stars tied the game at 1-1 four minutes into the second period as a shot by Dillon caromed off a stick and then the glass behind the net and hit Dubnyk in the back and bounced into the goal.
"It was a weird play. It happens," Dubnyk said. "There is nothing I can do about it."
Both teams had some very good scoring chances in the second, the best one coming at the end when Jordan Eberle made a nice deke on the power play that Lehtonen was barely able to deflect with his toe.
Dallas got another gift goal just 44 seconds into the third period as a long shot by Nystrom hit the hand of one of the Oilers on its way to the net, then appeared to strike Dubnyk in the mask before hitting the post and going in to make it 2-1 for the Stars.
The Stars have been incredibly successful against the Oilers since moving to Dallas, now holding a 55-13-4-2 record against Edmonton.
"It's up to us how well we do," Jagr said. "I don't think we have the kind of team that can allow itself to play up and down hockey. We are a good cycling team and we have the goaltending. Some of our games aren't going to be pretty, but as long as we win, it is fine."
Taylor Hall replied for the Oilers, who have lost six of their past seven.
Oilers coach Ralph Krueger said it was a case of some awful luck erasing what was otherwise a good effort.
"Those first two goals were two of the most bizarre goals I've seen in a long time, and back to back that way was tough for us to swallow," he said. "The result was painful to look at when you look at our execution for most of the game. For the first two periods, it looked like we were going to have our first real 60-minute game of the season. That second goal seemed to deflate us.
"We went back to some complicated habits after that and abandoned what had made us successful to that point."
Hall agreed that it was a much better effort than in the Oilers' 3-1 win over Columbus on Sunday, a game in which they were outshot 40-14.
"In Columbus, we didn't deserve the win and didn't play well," he said. "The way we played tonight is going to win us games."
Dallas had the best chance early as Cody Eakin had a partial breakaway but was stopped by a nice pad save from Dubnyk, who finished with 25 saves.
Edmonton got on the board first with seven minutes to play in the first period as Hall unleashed a deceptive off-stride wrist shot from the top of the circle that beat Lehtonen to the glove side.
The Oilers had another good chance to score with six minutes to play in the third on a power play but Lehtonen was once again there to rob Ryan Nugent-Hopkins with a glove save at the side of the net.
Dallas got an insurance goal while the teams were playing four-on-four as Jagr picked up a loose puck in the slot and spun around with a shot that beat Dubnyk. It was Jagr's fourth of the season.
The Stars put the game away for good with three minutes to play as Garbutt was able to chip a shot past the Oilers' goalie despite having defender Nick Schultz draped all over him.
"We are just trying to play hard right now," Lehtonen said. "We know we are not the most skilled team out there with the biggest names. We are a hard-working club, and everybody in this room feels we have a chance to win on any given night as long as we push ourselves. We have done well the last few games here and hopefully we can keep it going."
The Oilers made a surprise move before the game and decided to make veteran forward Ryan Smyth a healthy scratch. D Ryan Whitney was also benched for the third time in four games. The only significant injury for the Stars was forward Ray Whitney (foot), who is on injured reserve and expected to miss four to six weeks.
Copyright by STATS LLC and The Associated Press
Arena: Rexall Place Location: Edmonton, Alberta
Referees: Mike Hasenfratz, Kevin Pollock Linesmen: Mike Cvik, Mark Wheler
Attendance: 16,839 (100.0% full)
Team Stat Comparison
Power Play Goals
Power Play Opportunities
Shots on Goal
Taylor Hall (3)
Assist: Jordan Eberle
Brenden Dillon (2)
Assists: Stephane Robidas, Derek Roy