The Pirates tallied goals from Aubrey Hertzler and Tressa Swihart in the first half.
Algoma tied the contest at 2-2 early in the second half, but Elayna Dodson knocked in a rebound to put the Pirates back on top.
Hart made it 4-2 on a penalty kick from Faith Ramirez, but Algoma was able to trim its deficit to one goal with 3 minutes, 15 seconds left in the contest.
But Hart’s defense didn’t crack again, allowing the Pirates to hold on for the one-goal win.
Hart held a 16-6 advantage in shots on goal. Ramirez had two assists to lead the Pirates.
Hart will face the winner of Ravenna and host Big Rapids Crossroads for the district championship on Saturday at 10:30 a.m.