Combine first 4 ingredients in a small bowl; coat okra and potato in mixture.
Pour vegetable oil to a depth of 1/2 inch into a large heavy skillet, and place over medium-high heat until hot. Add okra and potato; reduce heat to medium. Cover and cook, turning often, 10 minutes or until potato is tender. Uncover and cook 3 more minutes or until browned. Serve immediately.