Sulaimon fired in 21 points and Curry added 17 as the Blue Devils (29-5) recorded the 2,000th victory in program history with a third-round decision over the seventh-seeded Bluejays.
Mason Plumlee scored 10 points for Duke, which earned a date against No. 3 seed Michigan State Friday at the Midwest Regional semifinals in Indianapolis.
Creighton (28-8) got 21 points and nine rebounds from Doug McDermott, but the star forward connected on just 4-of-16 shots from the field.
The Bluejays made just 2-of-19 3-point attempts.