British-born Tunnicliffe was ahead on overall points going into the final medal race, but the American needed a solid place to secure the top spot.
The 25-year-old was down as far as ninth out of 10 boats that qualified for Tuesday's final. Tunnicliffe says she spotted a wind shift on the third leg, fought her way up to third, and finished 11 seconds behind Volungeviciute to take the gold on total points after 10 races.