Kreider scored on a net-front redirection of K'Andre Miller's shot from the point to tie it 2-2 at 15:54.
The Rangers outshot the Stars 17-3 in the second period after Faksa's goal.
"We started playing more with the puck," Kreider said. "We cycled. We were coming at them in waves. We were doing a good job of not turning pucks over, getting pucks to the net quickly, supporting each other, moving our feet. We have to do that for a full 60."
The Rangers outshot the Stars 11-8 in the third period, but Khudobin's play in relief of Holtby, particularly his five saves on a Rangers' power play that started at 13:22, helped make the difference for Dallas.
"They both played great," Bowness said." 'Dobby' steps in in a very tough situation. All of a sudden they've got a power play and he made some huge saves for us. They both played outstanding."
The Stars also recognized the importance of the overtime win in their season opener because of what they endured last season, going 6-14 in games decided after regulation, including 4-8 in overtime.
They missed the Stanley Cup Playoffs in the Discover Central Division by four points.
"You want to get that off your shoulder right away," Stars forward Joe Pavelski said. "The extra points are huge. It was proven last year. You're in the NHL, you're playing teams that seem to get better every year. The skill level seems to go up and it's a fine margin. These points are important, especially when you get a 2-0 lead. You want to finish those games. We took a different route to finish it, but we got it done."
NOTES: Rangers defenseman Nils Lundkvist made his NHL debut, playing 14:19 with one shot on goal, five total shot attempts and three blocked shots. … The Rangers honored the late Rod Gilbert with a pregame ceremony that featured the Hall of Famer's wife, Judy, dropping the ceremonial puck. The Rangers players all wore white jerseys with Gilbert's No. 7 in warmups. They will wear a No. 7 patch all season. Gilbert died on Aug. 19. He was 80. … Defenseman Ryan Suter had an assist and blocked four shots playing 22:19 in his Dallas debut after signing a four-year contract July 28.