UCLA trailed by as many as 11 in the second half but Kevin Love, UCLA's top scorer with 22 points, sank a three-pointer with 17.7 seconds left to pull the Bruins within 80-79.
The Golden Bears then turned the ball over on the inbounds pass. Darren Collison's shot was blocked with six seconds left, and UCLA inbounded the ball to Shipp -- who got off a shot that nearly clipped the edge of the backboard before dropping through the hoop.
The Bruins clinched the regular-season title Thursday with a 77-67 overtime win against Stanford.
Ryan Anderson led Cal (15-14, 6-12) with 21 points and eight rebounds.