"He was seeing everything," Ottawa coach D.J. Smith said of Gustavsson. "He made every save he had to make. He made a couple of really big ones in the second when [Dallas] had that big push."
Brady Tkachuk and Connor Brown each scored his first goal of the season for the Senators (3-4-0), who ended a three-game losing streak. Drake Batherson and Tim Stutzle each had two assists.
Joe Pavelski scored, and Braden Holtby made 20 saves for the Stars (3-4-1).
"We gave them three goals by terrible plays on our part," Stars coach Rick Bowness said. "You can't give anybody three goals like we did tonight, but we're generating enough offensive chances to get us back into the game at the right times, but we don't capitalize."
Norris scored on the power play off a rebound created by Batherson's shot to give Ottawa a 1-0 lead at 5:49 of the first period.
"I think we're reading well off each other and, I guess, just keeping it simple," Norris said. "Playing with [Batherson] for I think my third year around now, you just got to be ready for the puck anytime."
Tkachuk made it 2-0 at 7:55 when he intercepted a clearing attempt by Stars forward Denis Gurianov. He snapped the puck through traffic and beat Holtby stick side.
"We had talked how good this team is in the first period and they can jump all over and you've got to be willing to play a north-south game," Smith said. "I thought we really did that in the first. [We] built ourselves a lead. And give them credit, they really pushed back in the end. But having the lead, we were able to hang on."
