Syracuse (19-4) recorded its most impressive road win of the season, handing Michigan State (14-11) just its second defeat at the Breslin Center this season.
Michigan State wasted a huge effort by Chris Hill, who scored 34 points, including a Big Ten Conference record 10 three-pointers.
The Spartans cut the deficit to 73-70 on a basket by Aloysius Anagonye before Anthony scored on driving layup with 2:29 left.
Anthony was undercut by Kelvin Torbert as he made an acrobatic layup and landed hard and awkwardly on his back. The freshman sensation lay on the ground writhing in pain for a few moments before rising to the floor and eventually converting the foul shot.
Hill sank his final three-pointer of the game with 70 seconds left to cut the lead in half and Alan Anderson made two free throws to make it a one-point game.
The Spartans would get another chance after Orangemen freshman Billy Edelin missed a 1-and-1 opportunity. Torbert missed a shot along the baseline and Adam Ballinger failed on a tip attempt before the ball landed in the hands of Anderson, who missed a shot in the lane that bounced away as time expired.
It was just the seventh road game for Syracuse, which split its first six.
Syracuse used a 14-5 spurt in the first half to take a 44-35 lead with 2:30 remaining. Hakim Warrick had nine points in the spurt, beginning with a three-point play. He added a jumper and a dunk and capped the run with a tip-in.
But the Orangemen did not score for the remainder of the half and the Spartans cut the deficit to 44-39 on two free throws by Erazem Lorbek and a basket by Anagonye.
Michigan State kept the momentum at the start of the second half, using a dunk by Anagonye and a three-pointer by Hill to draw even at 44-44.