On Friday, Georgetown Coach John Thompson III issued a declaration of desperation when he said, “Where we are now, we need a win.”

His charges responded in kind 24 hours later with a 64-60 victory over seventh-ranked Michigan State, getting 28 points combined from the starting back court of Markel Starks and D’Vauntes Smith-Rivera and a collective defensive gem in front of 12,561 on Saturday at Madison Square Garden.

Taking a break from their Big East schedule, the Hoyas (12-9) ended a five-game losing streak that had matched the longest in 10 years under Thompson and beat a ranked opponent for the second time this season. Georgetown resumes conference play armed with an infusion of confidence and with a schedule that includes teams from the bottom half of the Big East in four of the next five games.

The Hoyas limited the second-place team in the Big Ten to 39.6 percent shooting, forced 15 turnovers and held a 37-30 advantage in rebounding and 32-22 on points in the paint. Georgetown also made 18 of 24 from the free throw line, making good on a point of emphasis after the Hoyas shot 19 free throws combined over the last two games.

“I said to the guys before the game, ‘Let’s not come in here and have to listen to me give a speech after the game,’ ” Thompson said. “They went out, and we played hard. We have numbers back, and it makes a big difference.”

The Hoyas welcomed the return of center Moses Ayegba from an NCAA-mandated one-game suspension levied hours before tip-off of Monday’s 65-60 loss to No. 9 Villanova at Verizon Center. The senior served a nine-game suspension during his freshman year because of a pre-enrollment infraction, and the NCAA indicated to Thompson this most recent suspension was linked to that episode.

Georgetown also was able to call on guard Jabril Trawick for a second straight game. The junior (eight points, 4-of-6 shooting in 24 minutes) had started the first 14 games this season until breaking his jaw Jan. 8 during a 70-52 loss to Providence at Dunkin’ Donuts Center. Trawick missed the next five games before coming off the bench to play 12 minutes on Monday.

The starting front court also did its part Saturday after a string of games where it was conspicuously lacking on the stat sheet. Forwards Nate Lubick, Mikael Hopkins and Reggie Cameron combined for 23 points on 8-of-16 shooting with 13 rebounds, including eight offensive.

Georgetown went ahead for good on Cameron’s three-pointer with 19 minutes 42 seconds left, part of an 11-2 run. Gary Harris (game-high 20 points) got the Spartans within 50-48 with 3:30 to play, but Georgetown made 6 of 8 foul shots down the stretch in the third all-time meeting between the schools.

“Everybody came in and did a great job,” said Lubick, who had eight points, six rebounds, two assists, two blocks and a steal. “As Coach kind of touched on, [Michigan State] is a team that’s notorious for their rebounding and their physical toughness in the paint and their offensive rebounding specifically, and we beat them pretty good on the boards.”