"For some reason, they left me open," Joseph said. "Maybe they didn't see the last four or five go in. I was open for the shot and I knocked it down."
The No. 2 Orange improved to 24-1 overall and 11-1 in the Big East. Georgetown, which is ranked No. 12, fell to 18-5 for the year and 8-4 in the Big East.
The win gave SU coach Jim Boeheim his 880th career coaching victory, moving him past former North Carolina coach Dean Smith for third on the NCAA's Division I list.
Duke's Mike Krzyzewski is the all-time leader with 920 wins and former Indiana coach Bob Knight is second with 902 wins. Knight was on hand Wednesday as he partnered with Brent Musberger on ESPN's broadcast.
Boeheim has the most wins of any coach who spent his entire career at one school.
However, Boeheim was clearly not happy with his team following the victory. Georgetown had dominated the glass at both ends of the court, out-rebounding the Orange 52-35.
"A disaster for us," Boeheim called the Orange's rebounding performance.
The Orange survived its poor rebounding with a stellar defensive effort. Syracuse forced 15 Georgetown turnovers and scored 20 points off those miscues. Syracuse held Georgetown, which ranks second in the Big East in field-goal shooting, to 33 percent shooting from the field. In the second half and overtime, the Hoyas made just eight out of 30 shots.
"The only reason we won this game," Boeheim said, "is we hit a couple key shots late and our defense was good late."
Syracuse center Fab Melo scored 11 points, grabbed seven rebounds and blocked six shots. Melo hit double-figures for the third straight game.
But Joseph, who broke out of a recent shooting slump, saved the Orange. He had not made a 3-pointer in SU's last three games, going 0-for-8 during the stretch.
"The last couple games I wasn't making them, but I felt like I was shooting it pretty well," Joseph said. "The mechanics were the same. They just weren't falling."
Joseph had not made more than one 3-pointer in the last seven games. He was 3-for-27 from outside the arc since a 4-for-4 outing against Marquette on Jan. 7.
"Yesterday is the first day I can remember in a long time that he made a couple shots in practice," Boeheim said. "I was hoping that would be a good sign."
In regulation, Joseph's 3-pointer with 4:37 remaining gave Syracuse a 54-48 lead. He made one out of two free throws with 3:55 left in the game for a 55-51 advantage, but the Orange failed to score for the rest of the game.
Melo prevented the Hoyas from taking the lead, blocking Henry Sims' jumper with 29 seconds left to give Syracuse the final possession.
But the Orange didn't get a good shot. Scoop Jardine drove into the lane and flung the ball back to Dion Waiters, whose last-second shot was off-target from the moment it left his hand.
Syracuse made just three shots in the overtime. Joseph made two of them. Early in the frame he scored on a tough drive to the basket, tying the game at 57-apiece.
Then he stepped up to hit the game-winner in the final minute.
"He's been there all year for us," Jardine said. "He made the big shots down the stretch that we needed. Kris has always been steady with his 14, 15 points every game. That's why he's our leading scorer. That's why he's our go-to guy. That's why he stepped up today."