AJ Griffin came off the bench to score 18 points for Duke (5-0), which had too many weapons despite some early snags.
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Mark Williams added 14 points and 15 rebounds, Paolo Banchero scored 11 points and Trevor Keels had 10 points for the Blue Devils.
Kyle Jenkins, who had four of his team's seven 3-pointers, scored 18 points for Lafayette (0-3).
Moore poured in eight consecutive points early in the second half as Duke stretched its lead to 48-34.
Lafayette ended up with 17 turnovers, but 12 of those came in the first 15 minutes of the game.
After leading by 16 points, Duke led 35-27 at halftime despite making only 33.3% of its shots. The Blue Devils ended up at 45.6% for the game.
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The Blue Devils had too many scoring options for Lafayette to contain, particularly with reserves accounting for 30 points. The bonus for the Blue Devils was Griffin, who had a total of 12 points in the four previous games combined.
Duke's Mike Krzyzewski is receiving considerable attention as he's in his final season of a Hall of Fame career. So it was an odd situation for Lafayette coach Fran O'Hanlon, who's usually the more experienced coach than his counterpart.
O'Hanlon is in his 27th season as Lafayette's coach. He and Krzyzewski are two of five coaches with the same Division I team since the beginning of the 1995-96 season.
At age 73, O'Hanlon was the youngster compared to Krzyzewski, 74.
Duke completes a five-game homestand Monday night against The Citadel.