Luukkonen stopped 28 shots in Tuesday's 4-2 win over the Stars.
The 25-year-old took a shutout into the third period, but Dallas made things interesting late in the frame before an Alex Tuch empty-netter put the game away. Luukkonen has won back-to-back starts, but through five outings he sports just a 2-2-1 record with a 3.01 GAA and .903 save percentage.