Islacker's curling left-footed shot from 15 metres took keeper Katarzyna Kiedrzynek by surprise as the Germans won their first title since 2008.
Playing on German soil in Berlin's Jahn Sportpark, the competition's top scorer Celia Sasic made Frankfurt's early dominance count when she headed in following a deflected shot from captain Kerstin Garefrekes for her 14th goal of the season.
But they could not hold on to their lead as PSG scored following a clever corner that allowed Marie-Laure Delie to level with a header at the far post five minutes before the break.
With the game going towards extra time, Islacker stunned the French, who had never made it past the round of 16, to seal a third straight win for a German team after two consecutive wins by VfL Wolfsburg.
(Reporting by Karolos Grohmann; editing by Justin Palmer)
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