Pittsburgh also reached the final four with a 67-59 decision over Providence and Boston College was forced into overtime before eliminating St. John's, 82-75; and Connecticut defeated Seton Hall, 83-70.
Syracuse (24-4) captured all three meetings with Georgetown this season. Anthony averaged 26 points in the two wins in the regular season and did more damage in the third matchup to effectively eliminate the Hoyas from NCAA Tournament contention.
Anthony's two free throws gave the Orangemen the lead for good at 64-63 with 5:51 remaining. Hakim Warrick scored on a follow shot 35 seconds later for a three-point edge.
Georgetown (14-14) failed to convert several easy chances down the stretch. Gerald Riley missed a wide-open three-pointer with 2:50 remaining and the Hoyas trailing, 66-65. Riley also blew a layup with 1:52 to go as coach Craig Esherick clamored for a foul.
Despite their ineptitude, the Hoyas had a final chance to tie or take the lead after Duany split a pair at the line for a 69-67 lead with 33 seconds to go. But freshman Ashanti Cook's bounce pass to Mike Sweetney was dropped by Sweetney and wound up in the hands of Duany.
Syracuse freshmen Gerry McNamara and Billy Edelin each made two free throws in the final 20 seconds to seal the victory.
The Orangemen will meet Connecticut in Friday's semifinals.
Brandin Knight's jumper with 4:41 to go ignited a pivotal run as fifth-ranked Pittsburgh held off Providence.
Knight added two free throws in an 11-2 burst that turned a 51-49 deficit into a seven-point lead. Donatas Zavackas, who led all scorers for Pittsburgh (24-4) with 16 points, sank a three-pointer during the spurt.
Knight finished with 15 and Jaron Brown added 13 for the Panthers. Freshman Donnie McGrath led Providence (16-13) with 17 points.
Pittsburgh has won seven straight overall and six of its last eight Big East Tournament games.
Craig Smith scored 10 points in the overtime period to help Boston College avoid what would have been St. John's second straight surprising triumph. The Red Storm eliminated Notre Dame in the first round Wednesday.
Smith produced 33 points overall and converted a three-point play with 28.8 seconds remaining in regulation to force overtime.
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