The Midshipmen (4-8) made 5 of 6 free throws in the final 38 seconds to hold off the Tigers (7-5), who lost their fourth straight after their third-best start in school history.
Smith, in his first game since dislocating a knee cap in the season opener, had 13 points in the first half as Navy took a 32-24 lead.
Freshman Byron Hawkins came off the bench to score a career-high 23 points for Towson. Leading scorer Four McGlynn was held to nine points, five below his average. He had four points at halftime. He made two free throws with 31 seconds left then hit a 3 with 11 seconds remaining to pull the Tigers within 59-56.
Venturini's two free throws with 8 seconds iced it.