It was the second goal of the night for Peterson as the Muskies took a 1-0 series lead and stole home-ice advantage away from the Lancers.
Brock Boeser and Brandon Hawkins--playing in his first game back after an emergency appendectomy--scored the other goals for Sioux City.
The Muskies built a 3-1 lead heading into the third period but Omaha netted two, including one at the 3:39 mark, to force overtime.
Omaha and Sioux City face off in game two on Sunday at 5:05 PM.
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