Goodwin had seven rebounds and two steals for Memphis (9-2) in the Tigers' second win in a row.
Memphis jumped out to a 40-28 halftime lead and then held off Jackson State (4-8) in the second half. Memphis shot 44.8 percent from the field and won the rebounding contest 46-35.
Memphis also enjoyed a wide margin in free throws, sinking 19-of-32 from the line while Jackson State was 9-for-17.
Julysses Nobles led Jackson State, also known as the Tigers, with 20 points, and Brandon West notched 14 points and a dozen rebounds.