Rod Hall added 12 points for the Tigers (10-3, 1-0 Atlantic Coast Conference). It was their third victory in four games.
Olivier Hanlan led Boston College (4-11, 0-2) with 27 points, but missed the first of two free throws that could have tied it with 1.3 seconds left. Ryan Anderson had 13 points for the Eagles, who have lost seven of eight.
Trailing 62-59, Hanlan was fouled with two seconds left. He hit the first, but missed the second intentionally, grabbing his own rebound and getting fouled.
He then front-rimmed the first and had to miss second again, but McDaniels secured the rebound and the horn sounded.
Clemson had a 47-37 lead sliced to four points with just under seven minutes left on Anderson's jam, but Roper nailed a 3 from the right corner, Hall scored off a drive and the Tigers ended up making enough plays down the stretch.
BC closed an eight-point deficit to 59-56 in the final minute, but Adonis Filer hit a short post-up turnaround in the lane with 11 seconds left and McDaniels hit one free throw as the Tigers held on.
The Tigers led by 14 at halftime, but BC opened the second half by scoring the initial six points. Hanlan closed the spree with a 3-pointer before Tigers coach Brad Brownell called timeout. His team responded with consecutive baskets, pushing it to 35-23 on Jaron Blossomgame's dunk.
But the Eagles started to push the ball up the floor, getting into its offensive sets much quicker and made a 13-4 run to make it a tight game with 11:30 to play.
McDaniels then nailed a 3 to start a 7-0 spurt, pushing Clemson ahead 46-36 with just over eight minutes left.
In the first half, Clemson used a 16-6 run midway in en route to a 31-17 halftime edge, running off the floor after Roper nailed a 3-pointer at the buzzer.
The Tigers were far more physical and aggressive in the opening 20 minutes, mainly showing it with tight man defense. On one offensive possession they had four rebounds, with McDaniels capping it with a tip-in basket.
The Eagles had just four field goals and committed 10 turnovers in the opening half. During a number of possessions, they had trouble getting decent shots and found themselves running their offense about 20-25 feet from the basket with the shot clock winding down.
It was just the third time this season Clemson held a team under 20 points in the first half. The others were Stetson and Furman.
The Tigers were coming off their best non-conference start in three years.
BC is off until facing Virginia Tech on the road next Saturday. Clemson plays its next two at home, starting with Florida State on Thursday before No. 7 Duke next Saturday.
It was a matchup of the ACC's top defensive team, Clemson, against the league's worst.
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- Olivier Hanlan