With the score tied early in the final frame, Loui Eriksson gained control of the puck behind the net and fed a pass to Ryder, who was unguarded in the slot and whipped a shot past Jonas Hiller 6:42 into the period.
Nystrom added an insurance tally 7 1/2 minutes later and the Stars won for the fourth time in five games, surging into first place in the Pacific Division.
Richard Bachman turned aside 25-of-28 shots for the winners.
Hiller finished with 28 saves.
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