Arizona freshman forward Aaron Gordon went fourth to Orlando.
Then somebody with no U.S. college experience was selected. Dante Exum, the Australian point guard who will turn 19 next month, went fifth to the Utah Jazz.
The string of fresh-faced players was snapped when the Boston Celtics chose Oklahoma State sophomore point guard Marcus Smart with the No. 6 selection.
Two other freshmen went in the top 10. Kentucky forward Julius Randle was drafted No. 7 by the Los Angeles Lakers, and Indiana forward Noah Vonleh went ninth to the Charlotte Hornets.
Selecting 10th, the Sixers chose Louisiana-Lafayette junior point guard Elfrid Payton, but he was traded to Orlando for the No. 12 pick, Croatian forward Dario Saric.
Wiggins became the second consecutive Canadian taken first overall by the Cavaliers. Last season, the Cavs drafted Anthony Bennett of UNLV with the top pick.
This season, Wiggins averaged 17.1 points and 5.9 rebounds, and he was considered among the best athletes in the draft. He is the 11th international player drafted first overall.
"It's a great thing for Toronto, great thing for Canada actually," said Wiggins, whose father, Mitchell, played for Chicago, Houston, and the Sixers during six NBA seasons.
Parker had said the day before that he was going to be selected by Milwaukee, and he proved prophetic.
"I was just going with what I was given," Parker said. "They told me that they're all in."
In other deals, the Dallas Mavericks reacquired center Tyson Chandler and received point guard Raymond Felton from the New York Knicks for former Sixers center Samuel Dalembert; guards Jose Calderon, Shane Larkin, and Wayne Ellington, the Episcopal Academy graduate; and two second-round picks in this year's draft (34 and 51).
Yahoo Sports reported that Denver reacquired shooting guard Arron Afflalo from Orlando for guard Evan Fournier and the No. 56 pick.