Exum and Hood were expected to go sooner than they did in the first round of the draft.
Neither sounded disappointed, however.
"It's an unbelievable experience to be drafted and know where I'm going to live," Exum said from draft headquarters in Brooklyn. "It's just a crazy field. I can't wait to get to Utah and get to know the people and the fans and the team."
Hood averaged 16.1 points and 3.9 rebounds last season, when he was the Blue Devils' captain. He transferred to Duke from Mississippi State after the 2011-12 season, when he was named to the Southeast Conference's All-Freshman team.
"I'm very excited to get to Utah," Hood said. "… I've got a big chip on my shoulder right now and I'm anxious to get there."
Exum is a 6-foot-6 guard who does not turn 19 until July 13. In the weeks leading up to the draft, he was projected to be a top-four pick. But when Orlando surprisingly took Arizona forward Aaron Gordon at No. 4, it opened the door for Utah to select Exum.
Cleveland opened the draft by selecting Kansas freshman Andrew Wiggins. Milwaukee followed by taking Duke forward Jabari Parker, who reportedly had been a pre-draft target of the Jazz.
With the No. 3 pick, Philadelphia grabbed Kansas center Joel Embiid, whose potential outweighed the fact he broke a bone in his foot during a workout last week and will likely miss most of the 2014-15 season.
At No. 4, Orlando and coach Jacque Vaughn, a former first-round pick of the Jazz, the Magic selected Gordon.
Jazz fans attending the team's draft party at EnergySolutions Arena applauded the decision to pick Exum.
"I think it was a good pick," said Travis Cloward of West Valley City. "I think they needed another point guard or two guard."
Said Rob Harris of Farmington: "He has a significance chance to be a superstar because of he is very fast, a good defender and moves very smoothly with the ball."
Lowery Johnson of Kearns preached patience.
"Exum is young," he said, "and it takes awhile to transition to a higher-caliber game" like the NBA.
Mike Maples of Centerville hoped the Jazz would have moved up in the draft for Wiggins or Parker.
"This was the best we could we do considering we couldn't move up," he said. "It might take Exum a year to develop and for the Jazz to decide if they want Exum or [Trey] Burke to run the point."
Burke, who is also a point guard, was the Jazz's first-round pick last year. He went ninth in the first round.
The Salt Lake Tribune's Tierra Smith contributed to this story