Elko, who was the Atlantic Coast Conference coach of the year, guided the Blue Devils to a 9-4 season.
"This group is special and this program is special," Elko said. "Couldn't be more proud of this team."
Riley Leonard ran for two touchdowns and threw for 173 yards as Duke wrapped up its impressive season.
The Blue Devils have won four consecutive bowl games, although this was their first appearance in one since 2018. Jordan Moore ran for a touchdown in the first quarter, and then Duke took control in the second.
UCF (9-5) lost three of its final four games this season. John Rhys Plumlee managed only 28 yards passing in the first half and 182 for the game.
Moore opened the scoring with a 14-yard run, but Isaiah Bowser's 1-yard touchdown run for the Knights tied the game at 7. Duke outscored UCF 13-0 in the second quarter to take control.
After taking the lead on a short field goal, the Blue Devils recovered a fumble by Plumlee at their own 42. They went 58 yards in seven plays, and Leonard scored on a 1-yard run.
A 48-yard field goal by Todd Pelino made it 20-7 at halftime.
Down 23-7, the Knights had a good chance to get back in the game after a profitable exchange of punts gave them the ball at the Duke 32, but UCF turned the ball over on downs.
"That was a key drive. Obviously, we had the momentum," UCF coach Gus Malzahn said. "You've got to score right there."
The Knights finally scored again on a 2-yard run by Bowser with 9:03 remaining, but a trick play on a 2-point conversion failed badly.
READ MORE: Bowl game info, schedule for NCCU, Duke, UNC, NC State
Leonard completed the scoring with a 3-yard run with 2:29 to play. He finished with a team-high 63 yards on the ground.
After going winless in league play in 2021, Duke rebounded in a big way this year. The Blue Devils have not lost a game by more than eight points this season, the first time since 1953 they've made it through the regular season without losing by double digits.
"We didn't sell ourselves short in any way coming into this season. I think we set the bar high, and we wanted to achieve everything that we possibly could this year," Elko said. "There's going to be a big emphasis this offseason on continuing to build."
Elko is the second coach to have his team bowl eligible in his debut season at Duke. The other was Fred Goldsmith in 1994.
The Blue Devils reached nine wins in a season for the seventh time and first since 2014.
THE TAKEAWAY
Duke: An excellent ending to a very encouraging season. The defense in particular was strong against a good quarterback. The Blue Devils had six sacks.
UCF: Plumlee was limited by hamstring problems when the Knights lost to Tulane in the AAC title game. It wasn't clear if he was still feeling the effects Wednesday, but this was not a good performance by an offense that normally has little trouble moving the ball.
UP NEXT
Duke: Elko and the Blue Devils clearly have a lot to build on. They didn't lose a game all season by more than eight points.
UCF: It's off to the Big 12 for the Knights, who move from the American Athletic Conference to their new league. It was somewhat fitting that they played their final game this season at the home stadium of Navy - an AAC team.