Goodwin, a freshman forward from Atlanta, connected on 5 of 7 shots, leading five Tigers in double figures. Adonis Thomas scored 15 for Memphis (4-2), while Chris Crawford finished with 14 points, all in the first half.
Joe Jackson and Geron Johnson added 13 points apiece, with Jackson handing out eight assists.
Mike Liabo led Tennessee-Martin (2-5) with 21 points, hitting 7 of 13 shots, including 5 of 9 from 3-point range. Justin Childs had 17 points, while Myles Taylor finished with 16 points and nine rebounds.
Memphis, which was coming off a disappointing performance after splitting four games in the Battle 4 Atlantis tournament, played without starting forward Tarik Black, who did not dress for disciplinary reasons.
Memphis led 47-30 at the half behind 14 points by Crawford, who was 4 of 6 from outside the arc. Crawford connected on a long-range jumper at the horn to provide Memphis with its halftime advantage.
The Skyhawks, who have lost all six games in the series, were stymied by 12 turnovers in the half and a 38-percent shooting performance, although Tennessee-Martin did make four of seven shots from outside the arc.
Taylor had 11 points to lead Tennessee-Martin at the half.
The Skyhawks stayed close until about the midway point of the first half, but really never threatened after the break.
The Memphis lead would continue to swell, eventually reaching 41 with just under 9 minutes to play.
The Tigers caused 19 turnovers in the game, leading to 33 points. The Skyhawks shot 35.3 percent for the game (24 of 68), while Memphis converted 52.2 percent of its shots (36 of 69).
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