The Penguins won their fourth in a row while Dallas had a four-game winning streak snapped. The point the Stars earned, however, lifted them one in front of Colorado and Los Angeles for the final playoff spot in the Western Conference.
Michael Ryder tied it for the Stars with 12:37 to play.
Both sides produced two goals during the first three rounds of the shootout, but Dupuis managed a score in the fourth round while Ryder could not.
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