Kalin Lucas pumped in 29 points, going 9-of-13 from the field, including 4-of-5 from beyond the arc for the Spartans (4-1), who won the consolation game of the Maui Invitational.
Lucas returned from an apparent knee injury to make two clinching free throws with 1.5 seconds left.
Summers (12 points) connected on two long-range treys, giving Michigan State the lead with just over 2 minutes remaining.
Draymond Green also contributed 12 points for the victors.
Matthew Bryan-Amaning scored 15 points for Washington (3-2), which went down after also dropping a seven-point game to Kentucky at Maui.
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