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.
It's pretty crazy, but believe me when I say we didn't draft these players with the mindset we had to because they had good hockey-playing dads. It just turned out that way. But we're certainly glad they're a part of our organization.
— Arizona Coyotes director of amateur scouting Tim Bernhardt regarding the coincidence that six of the organization's top prospects are sons of former NHL players