The teams spent three days at Ramstein Air Force Base visiting with U.S. military personnel and then competed in Hanger 5, which was converted to a basketball facility for the special occasion. The game tipped off at midnight local time to accommodate its being televised live in the United States.
Connecticut built as much as a 15-point lead in the first half against the 14th-ranked Spartans, but Michigan State came back to take a brief lead inside the 6-minute mark.
The Spartans were within two points as the contest entered the final 30 seconds, but Keith Appling missed a shot that would have tied it with 20 seconds remaining.
Napier followed with two foul shots that gave the Huskies a 64-60 lead with 14 seconds left and his two additional free throws with a second remaining accounted for the final score.
Napier led the way for the Huskies with 25 points and Ryan Boatright added 13. Connecticut outshot Michigan State 46 percent to 37.
Appling scored 17 points to pace the Spartans.