Williamson had 32 points and helped rally the Blue Devils from behind in the final minute for a 77-76 victory Sunday to reach the Sweet 16.
Aubrey Dawkins finished with 32 points for the Knights, but his tip-in try just missed in the final seconds.
Duke coach Mike Krzyzewski "talks a lot about the basketball gods," a happy Williamson said. "They had our backs today."
Williamson was key to the comeback. He made a layup over Fall with 14.4 seconds left to draw Duke within a point as Fall fouled out on the play. Williamson missed the free throw, but RJ Barrett scored on a putback to put the Blue Devils (31-5) ahead.
Barrett said he had watched plenty of NCAA Tournament games where players missed foul shots and an offensive rebound could have made the difference.
"I was going to do whatever I can to get this rebound," he said.
Ninth-seeded UCF (24-9) had a final chance. Two of them, actually, from in close.
B.J. Taylor missed a short jumper, and Dawkins failed on his tip attempt with less than two seconds left, the ball spinning off the rim. Duke got the rebound, ran out the clock and moved on to the Sweet 16 for 27th time and fourth time in the past five years.
"It was up there forever, I felt like, in slow motion," Dawkins said.
Dawkins cringed at the miss. His father, Johnny, is the UCF coach and was a former Duke star and longtime assistant under Krzyzewski. The two coaches shared a long embrace at midcourt after it was over.
"It's tough," the elder Dawkins said. "I love that man. Without him, I wouldn't be where I am today."
Barrett finished with 16 points.
It looked as if Dawkins might take down his dad's alma mater in the NCAAs.
His last basket broke a 70-all tie, and when Fall dunked Taylor's miss -- the play was reviewed for a possible shot-clock violation -- the Knights were ahead 74-70.
UCF missed a huge chance to go up six when it couldn't connect on an alley-oop dunk attempt with 1:49 left -- Dayon Griffin's lob went off Dawkins' hands as he soared toward the rim -- and Cam Reddish came back with a 3-pointer for Duke. Taylor it made 76-73 with two foul shots with 45 seconds to go.
Williamson then missed a 3, but Duke grabbed the rebound and got the ball back to their high-flying freshman. Williams caught a pass left of the key and dribbled straight into Fall's 7-6, 310-pound frame.
Fall had stuffed Williamson three previous times, and Duke's young star was less effective underneath than he'd been his past four games. But Williamson got this shot to drop, shouting as he fell hard to the ground.
"I just tried to stay big and make a play," Fall said. "Obviously, I was in foul trouble, so I was being careful. But I just tried to make a play and make him miss and it didn't go my way."
When Duke dribbled away with the final rebound, Williamson and his teammates jumped in celebration and relief. They were moving on.
Duke will face fourth-seeded Virginia Tech in Washington, D.C., on Friday night for a spot in the Elite Eight.
Williamson, the game's most explosive player, was clearly affected by Fall. Who wouldn't be as the Knights senior stood 11 inches taller than Williamson and has a wingspan of 8-foot-4?
With Fall inside, Williamson went to the perimeter, hitting three 3-pointers after entering with just 18 on the season. When Fall was hit with foul trouble, Williamson charged to the hoop.
Fall finished with 15 points and six rebounds in his final college game.
Trailing 34-32 in the final four minutes of the opening half, Williamson hit a short jumper, and then collected Jordan Goldwire's miss for a three-point play. Barrett added a three-point play and Williamson threw a one-handed bounce pass to a streaking Jones for an easy layup as Duke led 44-36 at the break.
Williamson had 15 points in the first half, but had not dunked on the tall Fall -- mainly because UCF's center played just eight minutes due to foul trouble.
UCF: The Knights will have some big shoes to fill (size 22) next season with Fall's senior season complete. They also lose Taylor, the point guard who has started 101 of 104 games since arriving at UCF in 2014-15. UCF has a solid core of experienced starters returning, led by Dawkins, who was second on the team in scoring average at 15.1 points a game.
Duke: The Blue Devils have had too many tentative stretches in their first two games, but their overwhelming talent edge saved them against North Dakota State in the opening round and UCF in this one. Duke will need to be more consistent if it hopes to make a championship run.
COUNTING ON FRESHMAN
Duke's four freshmen carried the load against UCF. The quartet combined for 72 of 77 points in the victory, with Javin DeLaurier and Goldwire the only other scorers for the Blue Devils. "We're not deep," Krzyzewski said. "But we are good."
UCF's season is over.
Duke advances to play fourth-seeded Virginia Tech or 12th-seeded Liberty in the Sweet 16 at Washington, D.C., on Friday night.
More AP college basketball: https://apnews.com/MarchMadness and https://twitter.com/AP-Top25