D'Vauntes Smith-Rivera added 12 points and eight rebounds for the Hoyas (12-9), who held the Spartans to 40.4 percent shooting from the field and forced 16 turnovers.
Mikael Hopkins netted 10 points as Georgetown won for the first time since Jan. 11.
Gary Harris put in 20 points for the Spartans (19-3), who were playing without injured starters Adreian Payne and Branden Dawson.
Denzel Valentine provided 11 points and eight rebounds.
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