Gerald Henderson added 19 points for the Blue Devils (10-1).
It never looked like a matchup of top 10 teams as the Blue Devils were ahead 22-3 before Xavier managed its first field goal, a layup by C.J. Anderson 5:54 into the game.
Everything Duke tried worked, whether it was 3-point shooting or drop passes close to the basket that turned a short jumper into a layup.
Meanwhile, Xavier couldn't get anything right as passes flew out of bounds and shots missed by a mile.
Duke shot 61.8 percent from the field in the first half (21-of-34), including 8-of-15 from 3-point range. The Musketeers were 9-for-27 from the field, missing all four 3-point attempts, in the first 20 minutes — and they had 10 turnovers.
Scheyer had four 3-pointers in the first half, and his no-look bounce pass to David McClure for a dunk just seconds before the buzzer gave the Blue Devils a 55-24 lead.
Xavier scored the first seven points of the second half, but Duke coach Mike Krzyzewski called a timeout 2:26 in and the Blue Devils scored on a jumper in the lane by Henderson and got a 3 by Scheyer to put the lead back to 60-31 with 16:51 to go.
The win improved Duke's record at the Meadowlands to 18-1, the lone loss a 77-75 defeat to Arizona on Feb. 26, 1989. The Blue Devils' last trip here was another impressive win over a ranked team as top-ranked Duke beat No. 2 Texas 97-66 on Dec. 10, 2005.
Duke beat Purdue in its only meeting with a top 10 team this season and the Blue Devils have won 26 of their 37 games when both teams are ranked in the top 10.
Xavier was trying to match the best start in school history, as the 1996-97 team opened 10-0. The No. 7 ranking matches the highest in the program's history.
The Musketeers' only game against a ranked team this season was a 63-58 victory over Memphis in the championship game of the Puerto Rico Tip-Off.
This was the second-worst loss in Sean Miller's five seasons at Xavier. The Musketeers lost 77-55 to Arizona State on Dec. 15, 2007.
Duke has won all four games it has played against Xavier. The last one was a 66-63 victory in the 2004 regional finals of the NCAA tournament.