The Blue Devils, which improved to 14-2 overall, built on their 12-point halftime lead by making eight of their first nine shots to start the second half and shooting 53%.
Butler (16-3), playing Duke to improve its strength of schedule for selection to the NCAA tournament, couldn't stop the driving ability of Jones or the inside presence of Randolph, who made 11 of 13 shots.
Randolph, who also had 10 rebounds and four blocks, had his best game since his 23-point effort in his collegiate debut against Army to open the season.
No. 10 Maryland 75, North Carolina State 60 -- Steve Blake scored 20 points and Drew Nicholas made consecutive three-point baskets during a 14-0 second-half run that carried the Terrapins (13-4, 6-1) over the Wolfpack (11-5, 4-2) in an Atlantic Coast Conference game at College Park, Md.
Nicholas scored all 13 of his points after halftime as the defending NCAA champions solidified their hold on first place in the ACC with their 14th straight home win over the Wolfpack.
Arkansas trailed, 47-31, at halftime but fought back to 75-72 late in the game. But Tennessee outscored Arkansas, 17-7, the rest of the way to pull away.
No. 7 North Carolina 74, Virginia 54 -- Nikita Bell scored 13 of her 21 points in the second half and the Tar Heels (18-2, 7-1) pulled away from the Cavaliers (8-11, 2-6) in an ACC game at Chapel Hill, N.C.
La'Tangela Atkinson had 14 points and 12 rebounds for North Carolina. Candace, which forced Virginia into a season-high 27 turnovers.
No. 9 Louisiana Tech 102, Boise State 66 -- Trina Frierson scored 20 points and Cheryl Ford had 16 points and 14 rebounds to lead the Lady Techsters (16-2, 8-0) over the Broncos (4-14, 1-7) in a Western Athletic Conference game at Boise, Idaho.
Ford also had three blocked shots and Amber Obaze scored 16 points for Louisiana Tech.
No. 10 Purdue 82, Illinois 78 -- Erika Valek scored 20 points, including a pair of free throws with 18.7 seconds left, and the Boilermakers (17-3, 6-2) defeated the Illini (12-6, 4-4) in a Big Ten Conference game at Champaign, Ill.
Valek also had eight assists for Purdue, which has defeated Illinois nine straight times and 27 out of the last 29 meetings.
No. 13 Mississippi State 72, Alabama 56 -- Tan White scored 25 points in an SEC game at Starkville, Miss., and the Bulldogs (15-4, 4-2) ended an 11-game losing streak to the Crimson Tide (11-8, 1-5).
Mississippi State held Alabama to 25% shooting in the first half.
No. 14 Penn State 68, No. 23 Ohio State 53 -- Kelly Mazzante scored 26 points and the Nittany Lions (17-5, 7-1) defeated the Buckeyes (15-4, 6-2) at State College, Pa., to take the lead in the Big Ten race.
No. 16 South Carolina 78, Florida 64 -- Cristina Ciocan scored 18 points for the Gamecocks (15-4, 3-3) and made three of her team's season-high nine three-pointers in a victory over the Gators (8-11, 0-6) in an SEC game at Columbia, S.C.
No. 17 Vanderbilt 67, Auburn 66 -- Chantelle Anderson made a jumper in the lane with five seconds left and the Commodores (13-6, 3-3) erased a 21-point deficit to defeat the Tigers (14-5, 2-4) in a SEC game at Auburn, Ala.
No. 22 UC Santa Barbara 77, UC Irvine 58 -- Lindsay Taylor scored 18 points, including all 14 of her free throws, to lead the Gauchos (14-3, 7-1) over the Anteaters (11-7, 4-3) in a Big West Conference game at Goleta.