The woes continue for the Oilers (4-14-2), who have lost four in a row and gone 1-8-1 in their last 10 to slip to second last in the NHL.
It was the third consecutive home game the Oilers have been shut out, setting an unfortunate new franchise-worst record.
Edmonton has only scored two goals in its last five home games.
There was a good pace to start the game as the Stars controlled much of the early play, but the Oilers had by far the best chance to that point 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.
The game remained scoreless through the first with the Stars getting 11 shots on Edmonton goalie Devan Dubnyk and the Oilers responding with nine.
After the Oilers continued to squander power-play opportunities, including a lengthy 5-on-3 early in the second, Dallas took a 1-0 lead.
Peverley got a shot away and was then able to outmuscle defender Jeff Petry to get to his own rebound and chip his fourth of the season past Dubnyk from the doorstep.
The Stars came close to taking a two-goal lead on a power play with six minutes left in the second, but Cody Eakin rang a shot off the post.
Edmonton survived a pair of 5-on-3 penalty kills before the midmark of the third period and even a penalty-shot attempt by Valeri Nichuskin with three minutes remaining. But the Oilers couldn't get the equalizer they needed before Seguin dumped a shot from his knees into an empty net to give the Stars the 2-0 lead.
Roussel added yet another empty netter to ice the game.
The Stars are right back at it on Thursday night as they play the second game of a three-game road swing in Calgary. The Oilers return to the ice on Friday when they host the San Jose Sharks.
Notes - It was the first of three meetings between the two teams this season, with the Stars having claimed 11 of the previous 13 games they have played against each other. ... Dallas centre and former Oilers captain Shawn Horcoff made his first appearance against his old team since an off-season trade that sent him from Edmonton to the Stars in return for defenceman Philip Larsen. Horcoff played nearly 800 games for the Oilers in 12 seasons. ... Recently-signed free agent goalie 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 defenceman Justin Schultz still suffering from a groin injury, Corey Potter was called up and made his season debut. ... Stars winger Ray Whitney suffered a lower-body injury in his team's last game on Saturday and will miss at least the next two games. The veteran 41-year-old has recorded one goal and seven assists this season.