Leo Carlsson missed the game with a lower-body injury, Cutter Gauthier sat out with an illness, and Troy Terry missed his third straight game for Anaheim with an upper-body injury. All three participated in the morning skate on Tuesday and were game-time decisions.
Ducks coach Joel Quenneville said all three are day to day.
Roope Hintz scored, and Casey DeSmith made 22 saves for the Stars (27-11-9), who were coming off a 3-1 win at the Los Angeles Kings on Monday.
"We had a hard, hard game last night," Dallas coach Glen Gulutzan said. "Tonight, they were desperate. You could see that it was going to be a hard game. We have to be ready for those moments, right, because every team in the League right now is desperate for points."
The Stars played without one of their top defensemen, Miro Heiskanen, who missed his first game of the season because of a personal matter.
"We're hoping it will be short-term," Gulutzan said. "This is the first time we played without him this year, so you could feel it. You could feel that he wasn't in the lineup."
Shots were 2-2 at the halfway point of a scoreless first period before Anaheim finished with a 12-7 edge.
"They also had some guys missing, so it was a desperate team," Dallas defenseman Alexander Petrovic said of the first period. "They were all over us."
The Stars took their timeout at 2:27 of the second period before starting a 17-second 5-on-3, but four seconds into the two-man advantage, Jason Robertson was called for hooking.
Both teams were skating 4-on-4 when Dallas was called for another penalty while Anaheim had possession of the puck. Dostal left the ice for an extra skater and Kreider gave the Ducks a 1-0 lead at 3:36 after coming on, receiving a pass from Mikael Granlund and scoring with a snap shot from above the right hash marks.