The Ducks took a five-point lead with 3:56 to go, but were held to five points after that -- the last two coming at the buzzer after Arizona had clinched the victory.
McConnell gave the Wildcats a 62-60 lead with a 3-pointer and Nick Johnson hit 5-of-6 from the foul line down the stretch to protect the advantage.
Arizona recovered from its first loss of the season to win for the 22nd time. The Wildcats are 10-1 atop the Pacific12 Conference with UCLA holding down second place at 6-3.
California ended Arizona's bid for a perfect season last Saturday.
Johnson led Arizona with 18 points and Rondae Hollis-Jefferson contributed 14 points and 10 rebounds. The Wildcats won despite shooting 40 percent from the field and going 19-of-35 at the foul line.
Oregon (15-8, 3-8 Pacific 12) was led by 14 points each from Joseph Young and Jason Calliste.