Henry Torres scored the lone Muskegon goal in regulation off an assist from Marco Cuevas with 16:33 remaining in the first half.
Fremont scored on a penalty kick with eight minutes left in regulation to tie the game 1-1.
There was no more scoring through the rest of regulation and two overtime periods.
All five Muskegon shooters scored in the shootout session. The Big Reds sealed the win when goalkeeper Demetrio Lopez stopped a Fremont shot after taking over in goal during the shootout.
“I’ve seen him make some penalty kick saves in practices, and he made a big one tonight,” said Muskegon Coach Jeff Holmes about Lopez’ big save.
Muskegon will next play Ludington in the district semifinals at Coopersville on Wednesday at 4 p.m.