Brian Zoubek posted 14 points and 13 rebounds, helping to offset a poor shooting day for Duke's leading scorer Jon Scheyer, who was 1-for-11 from the field and 1-of-8 on three-point attempts to end with seven points.
The second-round victory netted the top-seeded Blue Devils (31-5) a matchup with the South Region's fourth seed Purdue, which outlasted Texas A&M in overtime for a 63-61 triumph.
Cal notched its first NCAA Tournament victory since 2003 with a 77-62 decision over Louisville in the first round on Friday.
It was a closely contested game in the early stages, as Duke opened up a seven-point lead behind a 12-5 run about 8 1/2 minutes in. Mason Plumlee and Zoubek took advantage of a pair of Cal turnovers to score the final two baskets of the sequence for an 18-11 score.
The Bears put in a bucket then capitalized on a Singler turnover to make it a one-possession game on Randle's layup moments later.
The Blue Devils were able to pull away again thanks to poor ball control by the Bears. Smith and Miles Plumlee dropped in layups on consecutive trips following a pair of turnovers to make it a seven-point game.
Smith then sank a jumper and Singler a three-pointer around a Cal bucket for a 29-19 affair with less than six minutes remaining.
Duke remained in control from there, finishing out the half with a Plumlee basket for a 37-24 lead heading to the locker rooms.
Cal continued to trail by double digits in the second half before Robertson drained a three almost five minutes in to make it 44-35.
A Boykin bucket a little more than two minutes later had the difference at seven, but Duke rattled off the next eight points -- the last a layup from Singler to extend the advantage to 52-37 nearing 11 minutes left.
Duke's 10-0 run a short time later essentially put the game away. Singler scored the first four points, Zoubek put in the next four and Smith's jumper with three minutes to play dropped for a 21-point difference, 66-45.
As a number one seed the Blue Devils are 39-8 all-time in this event and improved their overall record regardless of seeding to an impressive 90-30...The Golden Bears' all-time ledger in this event fell to 19-16...Duke was just 3-of-17 from three-point range, while Cal finished 3-for-12 from long distance...The Bears wound up shooting 39.6 percent from the floor...Duke connected on 47.4 percent of its shots...Cal had 11 turnovers compared with Duke's five.