In five appearances with the Stars during the 2012-13 season, Nilstorp went 1-3-1 while recording a 3.09 goals-against-average and .897 save percentage.
The 6-foot-3, 191-pound Nilstorp spent most of the season playing in the American Hockey League for the Texas Stars. He appeared in 39 games, going 19-13-3 with a 2.38 GAA and .907 save percentage. Nilstorp went 4-5-0 for Texas in the 2013 Calder Cup Playoffs, recording a 2.30 GAA and .922 save percentage.
In 2011, Nilstorp won the Le Mat Trophy with Farjestad BK in the Swedish Elite League. The Le Mat Trophy is awarded to the champions of the Swedish Elite League Playoffs. After going undrafted, Nilstorp signed with Dallas on June 5, 2012.