Sanders missed a last-second 3-pointer for Boston College after missing another jumper with 17 seconds left.
"We didn't play our best basketball, but we did when it counted," Singler said. "We made the plays when we had to. We showed good character."
The Eagles called a timeout with 5.5 seconds left to set up a final play, but Sanders' 3-point attempt bounced off the rim.
Boston College coach Al Skinner said Sanders' final shot was not what he called in the timeout.
"Obviously, we really didn't get to it," Skinner said. "What I was trying to get to, we weren't able to get to. So you have to credit Duke for their defense in that situation. We did not manage the last few seconds as well as we should have. That being said, Rakim still got the ball on the rim. It hit the front lip and had a very good chance of going in."
Rice said Duke's defense on the inbounds pass made it difficult for the Eagles to run their designed play.
"It was just a struggle to get the ball inbounds where we wanted to get the ball," Rice said. "So Rakim had to go get the ball and make a play."
Singler said the Blue Devils set up their defense to focus on Rice.
"We didn't want to allow Rice to get the ball," Singler said. "(Sanders) took a tough shot. We played good defense on him."
Duke trailed by eight points early in the second half before recovering on the strength of its 3-point shooting. Scheyer had four 3-pointers and Singler added three.
"It was big," said Singler of Duke's comeback. "But we need to play 40 minutes."
Henderson scored the winning points on a drive to the basket.
"I knew once I got it, I had to make a strong move," Henderson said. "I wanted to score the basket or get the foul."
Duke avoided the upset wave that already claimed two Top 25 teams in the tournament's first two days. Georgia Tech beat No. 17 Clemson on Thursday, and Maryland beat No. 8 Wake Forest on Friday.
Two ranked teams will meet in Saturday's first semifinal, No. 1 North Carolina and No. 22 Florida State.
Boston College recovered from a slow start to lead 29-22 at halftime. Sanders scored about 30 seconds into the game, and the Eagles went 8:10 before scoring again on a putback by Corey Raji.
Duke couldn't take advantage of Boston College's long scoring drought, leading only 11-2 on a 3-pointer by Singler before Raji's first basket sparked a 15-6 run that tied it at 17.
Duke made only 32 percent of its shots from the field in the first half as Krzyzewski said his players struggled to adjust to the Georgia Dome. Duke and North Carolina skipped Wednesday's practices at the facility.
"This was our first time shooting in this place," Krzyzewski said. "We were not able to get accustomed to the environment. Hopefully we're accustomed to it now."
The Blue Devils made 63.6 percent of their shots in the final 20 minutes.
Rice had only nine points in Thursday's win over Virginia, only his third game in single figures this season. He was scoreless before sinking a 3-pointer with 4:44 remaining in the first half, and he added another 3 with only a second left in the half.
Rice immediately turned to press row and yelled, "I'm not playing no more!"
Rice scored early in the second half to give Boston College a 34-26 lead, but Duke answered with four 3-pointers in the next 2:30, including two by Scheyer.
Duke led 57-49 after Singler's 3, but Trapani scored back-to-back baskets and Biko Paris added a 3-pointer with 4:44 remaining, leaving the Blue Devils with a 57-56 lead.