"He had a great performance," Gulutzan said about Lehtonen. "I thought he was the difference. ... Kari was our backbone tonight."
Gulutzan was promoted over the summer by general manager Joe Nieuwendyk from the Stars' AHL affiliate to succeed Marc Crawford, who was fired at the end of last season after the team missed the playoffs for a third straight season.
"It's a relief," Gulutzan said. "Now I know I can win one."
Lehtonen was at his best in the second period, making a series of sliding saves while Chicago built a 22-12 shots advantage, a total pumped up by three power plays.
"All the penalties seemed to be (against) us," Lehtonen said. "It was a tough task there, but the penalty-killing unit took most of the crazy chances away. It was a great battle. I was able to see the puck well tonight."
"By then, it was too late," Blackhawks coach Joel Quenneville said.
The teams will meet again Saturday night in Chicago.
"It's not the way we wanted to start the season, obviously," Chicago captain Jonathan Toews said. "I think we made too many mistakes and gave up too many chances. We've got to play with a little more energy."
Goligoski opened the scoring at 59 seconds of the second period on a one-timer from the high slot off a feed from Mike Ribeiro.
Benn made it 2-0 with 3:58 left in he second while the teams skated 4-on-4, backhanding the rebound of Sheldon Souray's slap shot past Crawford.
Benn contributed a crunching hit on Chicago defenseman Niklas Hjalmarsson with 14:51 left in the game, checking Hjalmarsson into the corner with such force that the collision broke a pane of glass.
Crawford gave the Blackhawks an early lift when he denied Benn on a breakaway just over 2 minutes after the opening faceoff. Crawford kept the game scoreless when he stopped Benn again from close range in the final minute of the first period.
Canadian businessman Tom Gaglardi, the front-runner to become the new owner once the Stars emerge from bankruptcy, watched the game from a luxury suite. ... Former Stars C Mike Modano received a standing ovation when he was shown on the big screen sitting in a luxury box during a break in the second period. Modano recently announced his retirement. ... F Adam Burish (groin), D Nicklas Grossman (hip) and D Adam Pardy (ribs) were out for Dallas. Chicago was without F Ben Smith (concussion), C Dave Bolland (upper body) and LW Viktor Stalberg (lower body). ... The Stars went 3-1 against the Blackhawks last season, but Dallas lost its final regular-season game at Minnesota, allowing Chicago to take the final Western Conference playoff berth.