Jaromir Jagr and Ryan Garbutt added insurance goals late in the third period as Dallas won its fourth straight visit to Rexall Place. The Stars are 11-1-0 in their last 12 meetings with the Oilers and 19-3-2 in their last 24. Overall, Dallas is 47-15-4-7 in 74 games against Edmonton since the move. The victory was their 759th in Dallas, one more win than they earned in Minnesota from 1967-93.
They're even more dominant in Edmonton -- the Stars are 28-5-2-2 in 37 visits since they moved from Minnesota 20 years ago.
Kari Lehtonen made 35 saves as the Stars won their fourth in a row.
"Kari's been great," Dillon said. "He's been our best player. Night in, night out he's been really great for us."
Devan Dubnyk made 25 saves for Edmonton, which lost the opener of a five-game homestand and has dropped six of its last seven.
"We have to focus on this homestand. We need to start getting some points at home. We have a big road trip coming up," said forward Jordan Eberle, whose team follows the homestand with a nine-game trip, making this homestand even more important.
Dallas broke a 1-1 tie on Nystrom's pinball goal 44 seconds into the third period. Nystrom fired a wrister from the high slot that hit the stick of Edmonton's Ryan Nugent-Hopkins, bounced off a surprised Dubnyk and went into the net for his first goal in 30 games, dating back to last season.
Perhaps the best news for the Stars was that they got three of their four goals from players who aren't among their top-six forwards.
"We need that," Dallas coach Glen Gulutzan said. "Depth is important in this League, and not every night your big guys are going to carry your team. They are going to do it most nights, but other teams have those types of players as well. Depth is really important.
"It's good for morale, the guys were hooting and hollering, calling those guys out and having some fun. When you get that secondary scoring, it can only benefit."
Jagr, who scored the overtime winner in Edmonton last week, made it 3-1 by rifling a wrist shot past Dubnyk with 4:35 remaining for his 669th career goal, moving him past Luc Robitaille into 10th place on the all-time list. Garbutt got the second of his career with 2:43 to play.
The Oilers scored the only goal of the first period on a brilliant individual effort by Taylor Hall. The first player chosen in the 2010 NHL Draft grabbed a pass from Eberle, raced through center ice, cut wide in the Dallas zone and fired a wrist shot past Lehtonen at 12:59 for his third of the season.
"I wanted to get more pucks on net," Hall said. "That's the reason I scored that goal. We need to continue to do more of that."
The Oilers outshot Dallas 11-9 in the opening period.
The Stars tied it 4:23 into the second period on a fluke goal. Dillon, a rookie defenseman, was credited with his second of the season when his shot hit Edmonton's Lennart Petrell, popped off the glass and deflected into the net off Dubnyk.
"It was a weird play," Dubnyk said. "It happens. Nothing I can do about it."
The goals by Dillon and Nystrom left Oilers coach Ralph Krueger shaking his head.
"Those first two goals are two of the more bizarre goals I've seen in a long time," he said.
Lehtonen preserved the tie with three big saves in the final 75 seconds of the period. With the Oilers on a power play, he stopped Sam Gagner on a rebound with 1:15 remaining, then denied a wide-open Hall at the left post 45 seconds later. Eberle then broke through the defense, but Lehtonen made his 15th save of the period by nudging his backhander just outside the post eight seconds before the final horn.
"He's been tremendous for us," Gulutzan said of Lehtonen. "What huge saves for us in the second period, end of the (second) off his toe. That game could have been a lot different. … We're blessed to have a goaltender of that caliber."
Material from team media was used in this report.