Clemson quarterback Tajh Boyd threw for 370 yards and five touchdowns and ran for another score to stun the Buckeyes, but two huge defensive plays late in the game ensured the Tigers would pull off the surprise victory.
The last of Boyd's scoring throws went six yards to Stanton Seckinger with 6:16 to play and accounted for the final score. That touchdown created the game's fourth lead change.
Ohio State had plenty of time to regain the lead and the Buckeyes reached the Clemson 46-yard line with 3:20 to play. But with Ohio State needing 13 yards for a first and the Buckeyes facing third down, quarterback Braxton Miller was hit by Breeland while trying to throw.
The ball popped in the air and was caught by Clemson's Spencer Shuey before it hit the ground.
That set up Clemson at the Ohio State 47, but Boyd made a potentially costly mistake with 1:33 to play when his pass was intercepted by C.J. Barnett.
Ohio State thus had another chance to pull out a victory, but two plays after the turnover Miller's pass was picked off by Anthony to seal the Clemson win.
Sammy Watkins and Martavis Bryant caught two touchdown passes each for the Tigers, who finished an 11-2 season in which they wound up second in the ACC's Atlantic Division.
Boyd completed 30-of-39 passes while Miller went 16-of-24 for 234 yards, two touchdowns and two interceptions.
The Buckeyes ended with a 12-2 mark, closing their campaign with consecutive losses to Michigan State in the Big Ten Conference title game and to Clemson.
The Big Ten wound up with a 2-5 record in bowl games this season, the two wins coming from Nebraska over Georgia and Michigan State over Stanford.
ACC teams have put together a 4-6 mark with Florida State yet to play in the national championship game against Auburn.