It's the first time in franchise history the Oilers have been shut out three consecutive times at home.
"You need to score to win games," Oilers coach Dallas Eakins said. "I thought early, we had some great chances that could have been easily converted. In the second I liked our structure, but I am not sure we had a shot 5-on-5. We had some zone time, but just couldn't get the puck to the net. In the third, we had a couple of chances again. But you have to finish and we couldn't do that."
Devan Dubnyk made 23 saves for the Oilers, who have lost their past four games and have one win at home this season.
The last time the Oilers scored at home was at 17:56 of the third period in a 4-1 loss to the Washington Capitals on Oct. 24.
Lehtonen was the reason for the Oilers scoring troubles early on. He made an outstanding glove save on Jordan Eberle in the first period, then got a piece of Sam Gagner's effort to direct it off the crossbar to keep the game scoreless.
"It was a little bit of a see-saw battle where special teams on both teams could have made a bit of a difference," Stars coach Lindy Ruff said. "It seemed like penalty killing prevailed. When they got some early power plays, they could have gotten some momentum when they scored and we could have put the game away later when we had our opportunities and we didn't."
In the second, the Oilers had a two-man advantage for 1:31, but were unable to beat Lehtonen. Edmonton went 0-for-5 on the power play.
Peverley scored the opening goal at 10:35 of the first period, beating Jeff Petry to a loose puck at the side of the net and lifting a sharp-angle shot over Dubnyk.
Going into the game, the Oilers had given up a League-high 75 goals. Defensively they were much better against the Stars, but could not generate much offense.
"The last three games at home, I don't know what it is, you are not going to win without scoring," Oilers center Ryan Nugent-Hopkins said. "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."
The Oilers have gone 182:04 seconds without a goal at home. They have just one win in seven home games.
"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.
"We need to have more sustained pressure. We have to get those gritty goals and those second opportunity goals with the tips and the rebounds, the way the majority of the goals are scored in this League."
In the third, the Stars had plenty of opportunities to put the game out of reach.
They had an extended two-man advantage, which they were unable to capitalize on. Valeri Nichushkin was also awarded a penalty shot at 16:56 after being hooked on a breakaway by Oilers defenseman Anton Belov. Nichushkin was denied by Dubnyk.
Eventually Seguin did ice the contest for the Stars, scoring from his knees into an empty net from his own end at 19:08. Roussel added another empty-netter at 19:46.
"I was tired and I aimed for the net," Seguin said. "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. It was one of those plays that if it goes it then great, if it doesn't then we would take a time out and get a quick rest."
Stars forward Shawn Horcoff was playing his first game back in Edmonton since being traded by the Oilers during the offseason. Horcoff spent 13 years in Edmonton, serving as captain for the last three.
"I think once it got closer to the game, I got a little bit emotional," Horcoff said. "I think the tribute was real nice and the respect from the fans was great. I'm just glad I got it over with and was able to get the win."
The Oilers had a tribute during a television timeout to Horcoff, who was traded to the Stars for a seventh-round draft pick and defenseman Philip Larsen.
"I didn't know what was going to happen, [reaction of the crowd]," Horcoff said. "You never know here. I've heard them boo a lot of quality players that have come back in this town. It was a nice show of respect and I appreciate them for it."