Oregon (13-3, 2-1 Pac-12) rallied to tie the game late in regulation and went ahead for good on Richardson's jumper with 17 seconds left in overtime.
Payton Pritchard, who played all 45 minutes, finished with 18 points, seven rebounds and six assists for the Ducks.
Nico Mannion led Arizona (11-4, 4-1) with 20 points and Josh Green scored 18. Zeke Naji had 11 points and 14 rebounds.
The Wildcats scored first in overtime but Richardson tallied the next five points for Oregon before Nico Mannion hit a 3-pointer to knot the game at 71-71 with 1:37 remaining.
Pritchard made the first of two free throws with 48 seconds left and the teams traded baskets before Richardson banked in the decisive shot.
Arizona had two chances at a go-ahead basket and rebounded both misses but then turned the ball over on an inbounds pass with 1 second left.
Arizona used a 9-0 spurt to take a 66-60 lead with under two minutes remaining in regulation, but Oregon scored the final six points of regulation, with Pritchard's short jumper knotting the game with 28 seconds left. Arizona played for a final shot but Zeke Nnaji misfired on a 15-foot jumper as time expired.
Behind Mannion's 10 points, the Wildcats built their lead to 29-18 in the first half before Dante scored inside on three consecutive possessions to bring the Ducks back within 32-26.
Arizona led 36-34 at halftime after missing seven of its last eight field goals to see its percentage fall to 45% while the Ducks climbed to 39% after that horrid start, with Richardson matching Mannion's 10 first-half points.
Oregon took its first lead of the game in the first minute of the second half when Francis Okoro dunked to finish a fast break. The Wildcats answered with the next seven points, but Oregon responded with an 8-0 run to go ahead 46-43.
Back and forth it went from there. Arizona edged its lead to five points but scored the next eight, including 3-pointers by Pritchard and Duarte for a 60-57 lead as the Wildcats took a timeout with 5:26 remaining.
BIG PICTURE
Arizona: It was the Wildcats' fourth straight loss to Oregon.
Oregon: The Ducks are 9-0 at home this season
ABSENT AGAIN
Oregon freshman C.J. Walker missed his second consecutive game with an ailing back. Prior to his injury, the 6-foot-8 Walker had started the previous six games and was averaging 5.7 points and 3.1 rebounds.