Poland's Klaudia Zwolinska picked up the silver medal, with Briton Kimberley Woods hanging on for the bronze after a thrilling climax that saw German reigning champion Ricarda Funk disastrously miss a gate on the very last run of the day.
French-born Fox came first in Saturday's heat but struggled in the semi-final, picking up two two-second penalties to see her through as the eighth of 12 finalists, but it was to be the only blip on her golden day.
Her face a mark of concentration at the start, the 30-year-old burst onto the course, aggressively attacking the early gates with a precision and power that had been noticeably lacking in her semi-final run.
The reigning world champion thundered through the second part of the course to take a commanding lead with a time of 96.08 seconds, cranking up the pressure on the rest of the field.
Briton Woods laid down a tremendously ambitious run to put herself into the medal conversation, but she was bumped into second place by Zwolinska in the second-last run before Germany's Funk made her descent in a grandstand finish.
Knowing the mark she had to beat, Funk set off at a searing pace and matched Fox's early spilt times, but a missed gate further down the course derailed her challenge in an instant.
The 50-second penalty incurred by that miss instantly destroyed any hope the German had of making the podium, and unleashed a burst of joy for Fox as she secured the second Olympic gold of her career following her C1 win in Tokyo.