"You try to stay even keel and not get too high about it," said Hedberg, who won his first game with the Stars to improve to 4-0 against Edmonton. "I have to be ready for the starts I get."
Hedberg made his season debut for the Stars after coach Dave Tippett gave Marty Turco his first night off in the team's fifth game.
A former backup in Pittsburgh and Vancouver, Hedberg spread out to make a save on pinching defenseman Steve Staios early in the second period to keep the Oilers off the board.
"Heady stole the show," said Ott, who scored at 11:45 of the third period after heavy traffic in front of Edmonton's Jussi Markkanen.
"I'm not pinning this on Ty," Oilers coach Craig MacTavish said. "We'll get him back in there before too long."
The Oilers had Markkanen on the bench for the final minute of the game and enjoyed a brief power play following a second straight minor penalty to Stars captain Mike Modano. But Hedberg held off the Oilers.
"Slow start again," Stoll said. "And Hedberg came up with some big saves."
With the Oilers trailing 2-0 in the second period, Smith gave the capacity crowd reason to cheer when he scored moments after Michael Peca missed on a chance for his first goal with Edmonton.
Rita scored his first of the season shortly after when he tipped a point shot by Marc-Andre Bergeron past Hedberg.
Oilers center Shawn Horcoff, who had six points in the first four games, injured his right shoulder in the second period and didn't return.
- Oilers RW Todd Harvey also sat out with a high right ankle sprain.
- The game was delayed in the second period as Hedberg was told he needed to replace the black tape on the end of his stick with white tape.