Rinne survived four Dallas power plays and made 32 saves to get a welcome victory for the Predators, who had lost four of five before taking the ice in Dallas.
Kari Lehtonen gave up four goals on 21 shots for the Stars, who lost their second game in a row.
Spaling's wrist shot opened the scoring at 7:44 of the first period and Clune gave the Predators a 3-0 lead on a penalty shot awarded when he was hooked on a breakaway by Jordie Benn.
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