Coming into Saturday afternoon's regular-season finale, teams were shooting just 30.4 percent on 3-pointers against third-ranked Arizona.
The senior guard scored a team-high 18 points off the bench and accounted for four of the Ducks' 10 3-pointers in a 64-57 win at Matthew Knight Arena in Eugene, Ore.
Oregon (22-8, 10-8 Pac-12 Conference) shot 52.6 percent from beyond the arc and finished the game on a 19-9 run over the final seven minutes.
Calliste's traditional three-point play at the 4:22 mark put the Ducks ahead 53-51 - their first lead since 2-0. He and Johnathan Loyd followed with consecutive 3-pointers to extend the advantage to eight with 2:44 left.
The Wildcats (28-3, 15-3 Pac-12) pulled within 61-57 on an Aaron Gordon dunk and free throw with 68 seconds remaining.
With 32 seconds left, UO sophomore forward Ben Carter blocked Nick Johnson's layup attempt and put the stamp on the victory.
Loyd added 16 points on 6-of-9 shooting.
After losing 8 of 10 games to open Pac-12 play, the Ducks rallied to win their final seven and perhaps punch their ticket for an NCAA tournament bid.
Arizona was paced by Gordon's 21 points and eight rebounds, but the team missed eight free throws, 9 of 11 3-point attempts and went more than seven minutes without a field goal during Oregon's push.
Johnson, a frontrunner for Pac-12 player of the year, was limited to 11 points on 4-of-12 shooting.
Despite the loss, the Wildcats will enter next week's Pac-12 tournament in Las Vegas as the No. 1 seed and will play the winner of the No. 8/9 game Thursday at the MGM Grand Garden Arena. The top four seeds receive a bye into the quarterfinals.
A game against a sold-out crowd - the first this season for Oregon - and a desperate team were not enough to overwhelm Arizona early.
The Wildcats raced out to a 20-8 lead by the midway point and had nine of their 11 first-half fastbreak points in the run.
The Ducks ran into a team that has let up very little this season. UO opened the contest 4 of 13 from the field and shot 37.5 percent in the half. But an 8-of-11 effort from the free-throw line kept the deficit manageable.
Trailing by 7 with 3:08 remaining, UO closed the half on a 7-2 run - capped by a Calliste 3-pointer in the closing seconds to pull within 31-29 at the break.
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