"He's one of the best in the league and he gives us a chance to win like that every night," Horcoff said.
The Oilers controlled the play in the scoreless first period, outshooting the Stars 11-9, and continued to squander power-play chances, including a lengthy 5-on-3 early in the second. Peverley then got Dallas on the scoreboard with 9:15 left in the second period when he knocked in a rebound of his own shot for his fourth goal of the season.
Seguin and Roussel had empty-netters 38 seconds apart in the final minute to seal the Stars' victory.
"I think in the first, we started real slow and we gave up a number of key opportunities and he made a couple of real, big saves that allowed us to get our feet," Horcoff said of Lehtonen. "Once we settled in a little bit, we were able to take the game over."
The Oilers have lost four straight and are 1-8-1 in their past 10 games. Edmonton was also blanked at home for the third consecutive game, setting a new franchise record, and has totaled only two goals in the last five on home ice.
"This is extremely frustrating, not to be able to put a puck into the back of the net," Oilers captain Andrew Ference said.
"It was one of these games again that you can point to positives, but at the end of the day you have to get the job done and score. It's obviously a huge challenge for everybody to keep their heads up right now and not grip their sticks too tight."
The Oilers had the best chance in the first period when Jordan Eberle got the puck in tight in front of the net, only to robbed by an impressive glove save by Lehtonen. Edmonton's Sam Gagner hit the crossbar two minutes later.
After Peverley's goal put the Stars ahead, they came close to taking a two-goal lead on a power play with 6 minutes left in the second, but Cody Eakin rang a shot off the post.
Edmonton survived two 5-on-3 penalty kills before the midmark of the third period and even a penalty-shot attempt by Valeri Nichuskin with 3 minutes remaining.
"The last three games at home, I don't know what it is," Oilers center Ryan Nugent-Hopkins said of his team's inability to score. "You are not going to win without scoring. We have to find a way to get the second and third opportunities.
"It's not a good sign. I thought we played pretty good in the last three games, we just have to find a way to score. This is not something you want to keep doing, putting yourself in this situation. I can't stress enough how we have to bear down in front of the net."
Seguin dumped a shot from his knees into an empty net with 52 seconds to go to double the Stars' lead.
"I was tired and I aimed for the net," Seguin said of his eighth goal of the season. "If it missed, I didn't care at that point. It was one of those shifts where we were out there for a solid minute at least. They were making some good plays and I just wanted to get it out."
Roussel added his empty-netter with 14 seconds left.
It was the first of three meetings between the two teams this season, with the Stars having claimed 11 of the previous 13 matchups. ... Dallas C and former Oilers captain Shawn Horcoff made his first appearance against his old team since an offseason trade that sent him from Edmonton to the Stars in return for D Philip Larsen. Horcoff played nearly 800 games for the Oilers in 12 seasons. ... Recently signed free agent G Ilya Bryzgalov has yet to join the Oilers as he has been sent to the team's AHL affiliate in Oklahoma City for a conditioning stint. ... With young Oilers D Justin Schultz still suffering from a groin injury, Corey Potter was called up and made his season debut.