Jason Robertson
scored his first NHL goal for the Stars (5-2-2), who are 1-2-2 since starting 4-0-0. Oettinger made 33 saves in place of Anton Khudobin, who was scratched due to team discipline.
"The guys did a really good job in front of me, limited their chances," Oettinger said. "Obviously, they have some firepower, they're very offensive. … You never know when you're going to get the call, so just happy to get the start and I just have to be ready at all times."
Dallas captain Jamie Benn said of Khudobin's absence, "We keep that inside the dressing room. Coach dealt with it, and we're moving on."
The Blackhawks and Stars will complete a two-game set in Dallas on Tuesday.
"We left a point on the board today, in my opinion, and we've got to get it back on Tuesday night," Stars coach Rick Bowness said.
DeBrincat, who had a goal waved off in the first period because of a high stick, gave the Blackhawks a 1-0 lead at 12:29 of the second period, shooting into an open net on the power play after receiving a backdoor pass from Dylan Strome.
"We had a really good start, first 10 minutes or so we were buzzing," Blackhawks coach Jeremy Colliton said. "A lot of energy and speed in the offensive zone. The game kind of settled down after that and it was a grind, but [our] power play came through for us. I thought the penalty kill (3-for-3) was really good."