Ahmed Hill misses the potential tying shot just before the buzzer. (Toni L. Sandys/The Washington Post)

Virginia Tech Coach Buzz Williams looked perfectly calm as his team trailed with 1.1 seconds left against Duke in Friday night’s East Region semifinal at Capital One Center. Why wouldn’t he be? His team trailed by just two and had possession underneath its basket. Williams had drawn up the perfect play to tie the game. Senior point guard Justin Robinson grabbed the ball and lobbed it to the rim for teammate Ahmed Hill.

But even as Hill grabbed the ball midair and had a wide-open layup to tie the game, he was quickly reminded of how cruel this game can be this time of year. His tip-in veered to the left as he was shadowed by Duke’s Zion Williamson, and he fell to the floor as the buzzer sounded. Williamson grabbed the ball and handed it politely to the ref before walking under the scoreboard, which read: Duke 75, Virginia Tech 73.

“I’m not even going to lie to you,” Williamson said. “When [Hill] caught it, I said, ‘We’re going to go to overtime.’ ”

The Hokies had not been to the Sweet 16 in 52 years, but then again they had never seen a player like Williamson either. The electric freshman finished with 23 points on 11-for-14 shooting and RJ Barrett added 18 for the Blue Devils, who will meet Michigan State in the Elite Eight on Sunday. Kerry Blackshear Jr. had 18 points for Virginia Tech, which was looking to keep one of the best seasons in school history alive.

Virginia Tech overcame a six-point deficit with 1:21 remaining and had several looks to take the lead in the final seconds. But the best was for Hill, who couldn’t convert and threw his hands up in protest afterward, looking for a foul on Williamson.

“It was a lob play that we ran a lot last year,” Hill said. “It was the first time we ran it this year. I saw that they switched. . . . Justin threw a great pass, and I just came up short.

“I tried to keep my eyes locked on the rim. It just bounced to the left.”

These two teams had met just over a month ago in Blacksburg, with the Hokies winning, 77-72, in a game that was more remembered for who didn’t play than who did. Duke was without Williamson, who was still nursing a knee injury. The Hokies were without Robinson, who had a foot injury that kept him out for 12 games. Both of those players were on the court Friday night, but the Blue Devils were without freshman forward Cam Reddish.

“We didn’t know until right before the game . . . [Reddish] had something wrong with his knee,” Duke Coach Mike Krzyzewski said.

The Blue Devils shuffled their lineup and leaned heavily on their two other freshman stars, Williamson and Barrett, to carry the load.

A key to beating Duke, as Williams explained earlier in the week, was to take more field goals attempts as a team than the Blue Devils. That would mean Virginia Tech was not giving up easy points off turnovers and in transition. It worked in the first half. The Hokies had two more field goal attempts and two more free throw attempts, even though Williamson impacted both ends with dazzling finishes and blocks.

Both teams slogged through offensive slumps late in the first half. Virginia Tech missed six of seven shots. Duke went the final 3:29 of the first half without a field goal, and after Barrett missed a free throw with two seconds left, Hill nearly banked in a desperation heave from half court. Williams belted out a big laugh on the sideline as it hit the front of the iron, with his team leading 38-34 as it ran back to the locker room.

Duke look determined as it returned to the court for the second half, with Barrett immediately attacking the lane for a quick score. That set the tone for a torrid pace the rest of the way. With Virginia Tech shadowing Williamson’s every move, Barrett found his rhythm in the second half. He scored 11 of the team’s 13 points through one stretch, including a coast-to-coast drive that he ended with an acrobatic layup to give Duke a 53-52 lead with 12:08 remaining.

The Blue Devils took the upper hand from there, seizing an eight-point lead thanks in part to Williamson finishing a thunderous alley-oop on a lob from guard Tre Jones. Virginia Tech pulled back within five after Robinson finished a three-point play following a layup and a foul, but Williamson again responded with a strong finish in the lane.

Virginia Tech again used a three-point play, this time from Blackshear, to trim Duke’s lead to 64-61 with just over six minutes left. The Hokies had a chance to get even closer on the ensuing possession, and Robinson looked as if he had a clean finish at the rim. But Williamson trailed from behind and violently blocked that attempt, and Jones finished a pullup jumper on the other end. Williamson made it 68-64 with another finish with 4:51 left. The Hokies got back within two on a pair of Blackshear free throws, but Jones again hit a three-pointer from the corner.

On the next possession, Williamson sent the overflowing crowd at Capital One Arena to its feet one last time. He delivered a spin move in the post and elevated for a two-handed slam, flexing and huffing once he landed.

Still, just as it had done in games all season, especially without Robinson, Virginia Tech figured out a way to position itself to win. It trailed by six with 1:21 left, but Blackshear and Robinson each scored to cut it to 75-73, and Duke missed a crucial free throw that gave the Hokies a chance in the final seconds. Hill air-balled a three-pointer, but Blackshear came up with a decisive offensive rebound before Williams called a timeout with five seconds left to draw up one final play. Guard Ty Outlaw missed a three-pointer out of the timeout, but Duke knocked the ball out of bounds with 1.1 seconds left. Then came the final miss.

“To even be in that position obviously is a lot of work,” Williams said. “But if we were to replay it again right now, I would call the exact same plays because of my faith and trust in those guys.”