Gonzaga took a one-point lead when Kelly Olynyk sank two free throws with 4.6 second left and Butler's chances dimmed further when Alex Barlow was called for traveling.
But Jones then stole an errant inbounds pass at midcourt, streaked to the other end of the court and connected on a one-handed shot from near the foul line as time expired, handing Butler (16-2) an improbable victory.
He finished with 20 points and Kellen Dunham added 14 as Butler notched its 13th straight win, despite the absence of injured leading scorer Rotnei Clarke.
Elias Harris and Sam Dower each supplied 20 points for Gonzaga (17-2).
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