Raffi Torres also scored for the Oilers, who've won three straight and are 8-2-1 in their last 11 games. The Oilers had a rare successful visit to Dallas behind Roloson's 21st career shutout. They improved to 4-19-2 in regular-season games in Dallas since the Stars moved from Minnesota in 1993.
Stars goaltender Marty Turco was coming off back-to-back shutouts, but the Oilers capitalized on a two-man power play midway through the first period and never allowed Dallas to gain any momentum. Turco finished with 13 saves.
With one second left on the two-man advantage, the Oilers got the game's first goal when Bergeron's blast from the top of the right circle got through Turco's pads at 11:13 of the first period.
Turco's shutout streak ended at 154 minutes, 19 seconds.
Torres struck from the slot at 2:51 of the second period.
Edmonton started the night as the league's top penalty-killing team, and the Oilers showed why when they kept the Stars scoreless over two minutes of a 5-on-3 Dallas power play in the second period. Dallas failed to convert on five power-play chances.
The Stars, shut out for the third time this season, were minus four of their top forwards: leading scorer Mike Modano (hip flexor/groin injury), captain Brenden Morrow (groin), Eric Lindros (bruised foot) and Antti Miettinen (lower-body).
Out for the Oilers were Ryan Smyth (fractured right thumb), Ethan Moreau (dislocated right shoulder) and Ales Hemsky (right shoulder).
Notes: Edmonton has allowed one goal in its last three games. . . . Dallas RW Chris Conner was called up from Iowa of the American League and made his NHL debut. . . . Roloson had his third shutout of the season. . . . Stars D Darryl Sydor, an Edmonton native, was sworn in as a U.S. citizen in Dallas earlier this week. . . . Dallas had killed 15 straight short-handed situations before Bergeron's goal.