The Blue Devils, seeded No. 1 in the West Region, held a 53-47 lead less than 4 minutes deep in the second period. Arizona then went on a 20-2 run that ended Duke's hopes for a repeat title.
Two free throws by Jones put Arizona in front for good at 55-53 with 15:18 to play.
Arizona, seeded fifth in the region, will take on third-seeded Connecticut Saturday with a trip to the Final Four on the line.
Derrick Williams scored 32 points to lead Arizona (30-7), which made 53 percent of its shots from the field and hit 9-of-15 attempts from 3-point range. Williams was 5-of-6 from beyond the arc and also grabbed 13 rebounds.
Jones scored 16 points and Solomon Hill had 13 for the Wildcats.
Duke got 28 points from Kyrie Irving and 18 from Kyle Singler. After having spent part of the season on top of the national rankings, Duke completed its campaign at 32-5.
The Blue Devils were the second No. 1 seed to be eliminated from the tournament, joining the Pittsburgh Panthers. Two more No. 1 seeds remain in Kansas and Ohio State, who will play Friday.