Nilstorp was the backup to Richard Bachman before Tuesday's move. Bachman has made three straight starts since he had to replace starter Kari Lehtonen, who re-injured a groin early in a win over the Los Angeles Kings on April 9.
Bachman helped the Stars finish off a season-best five-game winning streak before Monday night's 5-2 loss to Chicago.
Nilstorp has bounced between Dallas and the Texas Stars most of the season. He's 1-3-1 with Dallas and 18-11-5 with Texas.
The Stars have two days off before playing Vancouver at home on Thursday night.
He is, in my opinion, one of the best defensemen in the NHL and continuing to grow. I think his game, from an offensive standpoint, he continues to drive our offense... I think there's still tremendous upside for Oliver.
— Coyotes GM Don Maloney on defenseman Oliver Ekman-Larsson