Fellow freshman Justise Winslow added 13 points and 12 rebounds for Duke (31-4), which for the second straight tournament game ran out to a quick lead and stayed in control the rest of the way.
Duke — holding a No. 1 seed for the 11th time in 18 seasons but its first since 2011 — advanced to face fifth-seeded Utah in Houston's South Region semifinals.
Mike Krzyzewski's Blue Devils are pushing for their 12th Final Four and completed their two-game stay in their home state with a pair of hot-shooting wins.
Duke shot 55 percent against the eighth-seeded Aztecs (27-9), two days after shooting 63% against Robert Morris.
Fittingly it was Okafor, the big man who has powered Duke's offense all season, who led the way Sunday.
The 6-foot-11 freshman showed a full range of elite moves in the opening half. He scored with his back to the basket. He put the ball on the floor from about 10 feet and drove for scores. He ran the court for a dunk on a beautiful Cook-to-Jones-to-Okafor push downcourt.
The Aztecs, despite having some size to wrestle with him, had no way to stop him.
Meanwhile, Winslow put on his own show with five assists and one jaw-dropping block on JJ O'Brien at the rim. That set the ball loose in transition for Quinn Cook to bury a three-pointer, then pretend to holster pistols as he turned to run back up the court — a sign that the Blue Devils were completely at ease and rolling with a confident strut.
The Aztecs were trying to reach the Sweet 16 for the third time under coach Steve Fisher, but San Diego State — with a few players and coaches battling a stomach ailment — got off to a bad start and struggled to get Duke to slow down early.
Duke shot 53% to lead 37-24 at halftime. The Aztecs fought back within 44-37 on a three-pointer from Malik Pope with 12:42 left, then got the ball back with a chance to inch closer.
But Trey Kell missed an open shot in the lane, and Duke pushed the ball back downcourt for a three-pointer from Cook — a crushing five-point swing and the start of an 11-0 run that killed any chance for San Diego State to get back in it.
Winston Shepard scored 13 points to lead the Aztecs, who shot just 33 percent.