He came into the game shooting just 21.6 percent (8-for-37) on 3-pointers this season.
"When you have your back against the wall, that's when you get tested and see what kind of player you are," Shipp said.
Collison went 3-for-6 from the field and 7-for-7 from the free-throw line in the second half. He finished the game 6-for-9 from the field and 9-for-9 from the line, giving him a school-record 40 consecutive free throws.
"The second half was a bit of a struggle but we got it together," Collison said. "That's what you're going to have when you're on the road but you have to remain together."
The Bruins lost most of their 40-29 halftime lead when the Ducks went on a 9-2 run early in the second half.
A three-point play by Joevan Catron started Oregon's rally, followed by a layups from Matt Humphrey and Catron and runner in the lane by Porter that cut UCLA's lead to 46-43 with 14:48 left.
But the Bruins scored the next five points on a layup by Collison and a 3 by Shipp to extend the lead to 51-43.
Oregon again cut the deficit to three points as Porter banked in a short jumper, Kamyron Brown hit a 3-pointer and Porter made a floater to make it 53-50 with 11:32 to play.
The closest the Ducks would get after that was when Porter drained a deep 3 with 6:09 left to make it 64-60. But over Oregon's next four possessions, Porter missed three 3-point attempts and turned the ball over twice.
"A few times we were right there, but they didn't let us close the gap," Oregon coach Ernie Kent said.
The Bruins scored the next eight points, including Shipp's final 3-pointer of the game, to take a 72-60 lead with just under 3 minutes to play.
"You knew they were going to make their run," UCLA coach Ben Howland said. "The building was alive, and I wish for once we could show up here and not have the building so ready for us. It's a great crowd, a great college basketball atmosphere."
Shipp helped neutralize any advantage Oregon had from the crowd.
"He is that type of kid," Howland said. "He feeds off the energy to quiet the crowd with a big shot. He's been doing that since I've coached him, and he enjoys that. It's his personality."
Alfred Aboya and Nikola Dragovic both had 12 points for the Bruins.
Catron added 13 points for the Ducks and LeKendric Longmire had 10.
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