Shelden Williams added 16 points, 11 rebounds and nine blocks for the Blue Devils (13-0, 3-0 Atlantic Coast Conference).
Duke, one of four unbeaten Division I teams in the country, struggled to put away the Cavaliers (9-5, 0-4) but still won for the 20th time in 22 meetings.
Sean Singletary scored 21 points to lead the Cavaliers, who fell to 0-4 in the league for the first time since the 1998-99 season, Pete Gillen's first year as coach. Virginia has not won at Cameron Indoor Stadium in 10 years.
The Blue Devils had a scare late in the first half when Daniel Ewing went down during a scramble for a loose ball with an apparent left ankle injury. Ewing returned to play all 20 minutes in the second half, finishing with 17 points.
With Duke holding a 34-28 lead at the break, Redick went 6-for-7 from the field and 4-for-4 from behind the arc in the second half to help the Blue Devils gradually increase their lead.
In a three-minute stretch, Redick hit three 3s, two off feeds from Sean Dockery. Redick closed that run with an excellent move on the wing, spinning away from Singletary and making the shot for a 65-50 lead with 7:55 left.
Williams certainly did his part, providing the rugged complement to Redick's smooth perimeter game. He repeatedly rejected shots by both penetrating guards and post players attacking the offensive glass.
His nine blocks surpassed his previous career high of eight set against Wake Forest last season.
Duke got off to a slow start, trailing by seven early before Ewing got the Blue Devils going. He scored 10 points in the first half, all during a 20-6 run that pushed the Blue Devils to a 30-23 lead.
Redick's big night was the highlight of a game that featured the return of junior Shavlik Randolph, who missed the past four games with mononucleosis. Randolph had a basket and two blocked shots in five minutes, but his return promises to improve the depth of a team that had just eight recruited scholarship players coming into the season.