Parker had his third straight 20-point performance and also got 10 rebounds. He became the first freshman in coach Mike Krzyzewski's 34 seasons at Duke to begin his career with three consecutive 20-point games.
Andre Dawkins had 17 points with his first five 3-pointers of the season for Duke.
The Blue Devils (2-1) shot 55 percent, made 12 3s and never trailed. They bounced back from a 94-83 loss to No. 5 Kansas by making quick work of the outmanned Owls.
Pablo Bertone had 17 points to lead FAU (1-2), which shot 37 percent and lost its second straight.
The Blue Devils had little trouble claiming their 103rd straight nonconference win at Cameron Indoor Stadium. The last non-ACC team to beat them there was the 2000 St. John's team whose coach, Mike Jarvis, is now in charge at FAU.
The lopsided victory came a few hours after two of the nation's top high school players — Minnesota point guard Tyus Jones and Chicago center Jahlil Okafor — gave nationally televised commitments to play at Duke next year.
Hood was held to 11 points on 3-of-8 shooting in the loss to the Jayhawks three nights earlier that had Duke smarting.
In this one, the Mississippi State transfer was the most dominant player on the court and once again put up big numbers against an Owls team that for a while had trouble outscoring him — let alone the rest of the Blue Devils.
Hood finished with his third career 20-point game and his second in a three-game span with Duke. He was 8 of 11 from the field and 12 of 13 from the free-throw line, making his first five shots and hitting all nine of his foul shots in the first half while helping Duke put the Owls away early.
Hood's bid for a perfect night ended when he rimmed out a 3-pointer with 5 seconds left in the half and Duke up 52-29.
Dawkins got going in his most extensive playing time since his return to the team. He spent last season away from organized basketball while he continued to grieve his sister's death in 2009, and had played two total minutes in Duke's first two games.
His first 3 — which sent the Cameron Crazies into ear-splitting delirium — capped a 17-3 run that pushed the lead into double figures to stay and included four 3s by four different Blue Devils.
Shortly after that, Hood reeled off 12 points during the 18-5 burst that made it a 20-point game to stay.
Justin Raffington finished with 14 points for FAU.
There were a few ties between the otherwise dissimilar programs: Owls associate head coach Mike Jarvis II was Duke's director of player development from 2004-06, and assistant Tim Kaine is Krzyzewski's godson.