With the victory, the Tigers (19-10, 10-7 Atlantic Coast) can clinch the fifth seed in the ACC tournament with a win Saturday over Pittsburgh. Clemson was picked to finish 14th in the league before the season started. The Tigers can also win 11 league games for the first time in 61 ACC seasons.
The Tigers, the second best free throw shooting team in the league, missed back-to-back 1-in-1s in the final minute. But Landry Nnoko blocked a shot that could have pulled the Hurricanes within two and Jaron Blossomgame pulled down an offensive rebound on Damarcus Harrison's miss to let the Tigers hold on.
Rion Brown led Miami (15-15, 6-11) with 21 points. The Hurricanes will likely need a win Saturday over Wake Forest to get an ACC tournament bye.
With the game tied at 29 early in the second half, Clemson would score on its next four possessions to take the lead for good. Damarcus Harrison hit a 3-pointer, Adonis Filer and McDaniel followed with short jumpers and Filer buried a 3 to put the Tigers ahead 39-32 with just under 14 minutes left.
The Hurricanes kept hitting shots to stay in it, but couldn't quite catch up.
Miami shot 50 percent from the field (25 of 50), becoming just the fourth team to hit at least half their shots against the second-best defense in the country. It was the first time the Tigers have won one of those games.
Clemson still seems a long shot for an at-large bid for the NCAA tournament. The Tigers don't have a quality non-conference win, and their only victory over a team likely to be in the tournament is a 72-59 home win over Duke. A victory over Pitt and a run to the ACC tournament semifinals or finals would go far to help Clemson's chances.
K.J. McDaniels scored 12 points and had nine rebounds, while Harrison also scored 12 for the Tigers.
Erik Swoope scored 14 points for Miami, while Garrius Adams added eight points and five rebounds.
Miami hit nine of its first 12 shots of the game, and the Hurricanes led 19-12 on Davon Reed's 3-pointer with 11:29 left in the first half.
But Clemson scored the next 11 points, including a five-point possession when Rion Brown was called for a flagrant foul on Damarcus Harrison. Harrison hit both free throws, then buried a 3-pointer.
Neither team would lead by more than four points the rest of the half. It was tied at 27 at the break.