Joaquim Gomes had 18 points and 11 rebounds to lead the Crusaders (13-12).
Whether knocking down open 3s off passes around the perimeter or kickouts from the post, Duke found plenty of openings along the perimeter. The Blue Devils went 15-for-26 from 3-point range - many coming against a first-half zone by Valparaiso - and shot 48 percent.
Even Randolph and Nick Horvath - reserves who were 0-for-12 from behind the arc this season - got into the act. Randolph hit two 3s during Duke's initial burst, while Horvath drained one in the second half.
"Most people haven't played us zone because we can shoot," Duke coach Mike Krzyzewski said. "I wouldn't say we're like a 3-point shooting team, but if you're going to give it to us, we'll shoot them and I think we can make a pretty good percentage of them."
The Crusaders had won nine of 11 coming in, but got off to a shaky start even before the opening tip.
During the national anthem, the team and the assistant coaches turned to face the American flag in one end of the arena, while head coach Homer Drew - and everyone else in Cameron Indoor Stadium - faced a flag presented at midcourt.
Once the game started, the Blue Devils hammered the Crusaders with a barrage of 3-pointers in the opening 11 minutes to prevent any chance of an upset. They shot 10-for-16 from behind the arc in the first half in taking a 53-29 lead.
Facing a zone for much of the half, Duke hit nine of its first 13 shots behind the arc, ending with Ewing's 3 from the left wing, for a 39-13 lead with 9:15 left in the half.
"I think the difference in the game happened too early on us," Drew said. "If they could've been just human for a while and missed some of those, it would've helped us stay a little bit closer, which would've helped us with our confidence."
The Blue Devils got contributions from just about everywhere.
Shelden Williams, a 6-foot-9 center, assisted on three 3-pointers, kicking the ball outside when Crusaders defenders collapsed. The sophomore - who was 1-for-3 from behind the arc this season - also drained a 3 off penetration from Deng, sending the Cameron Crazies into a frenzy.
Randolph, a 6-10 reserve, added two 3s despite shooting 0-for-7 behind the arc this season.
"This team's has a lot of good shooters on it, and if me and Shelden are stepping out and hitting 3s, that's tough to defend," Randolph said.
Redick had a four-point play, draining a 3 in transition and drawing a foul on Greg Tonagel for a 34-13 lead. Ewing then followed with a dunk off a turnover and a 3, capping a 12-0 run.
Valparaiso got no closer than 16 points after that.
The Crusaders shot 31 percent and committed 16 turnovers that led to 23 points by Duke.
"We really focused a lot on defense," Deng said. "We didn't go over our offense a lot. With our big guys hitting shots, it just seemed like everything was going in. It makes you want to play defense more."