UCLA forward Travis Wear converted a go-ahead lay-up with five seconds remaining, and Oregon's Johnathan Loyd couldn't respond with a basket.
Oregon coach Dana Altman described the final play as a "bad read". Loyd was blocked on a fade way that would have tied it.
"We were hoping he'd make a play for Joe. I'll have to look at the tape, but that's not what we had planned," he explained following the loss.
Down 11 points with 6:10 to go, Oregon went on what might have been a season-saving run. The run made up the lead and gave them a three point edge with 1:14 remaining. But the season was not saved, and now Oregon is in a precocious situation.
"It was a big opportunity, especially when we came from back. That would've been a great opportunity for us. But now it's battle back," Altman said.
Young finally broke out of his slump to dump 25 on the Bruins, but the effort wasn't enough.
"I just stayed in the gym. My teammates were getting better, coaches were getting me better. If you stay in the gym consistently, you'll get out of the slump quick," he explained.
Richard Amardi grabbed a Kyle Anderson miss on UCLA's final possession, but UCLA was able to tie him and force a jump ball with the possession arrow in their favor. Wear would score three seconds later.
"We've just go to get the rebound at the end. We had three rebounds that we didn't get, and that's just those toughness plays that we didn't get. We've just got to get tough," said Young.
UCLA had seven second half offensive rebounds that turned into eight points.
Mike Moser was held scoreless for the first time all season. He took just two shots and turned it over five times in 14 minutes.
"He's had a really bad stretch here in the conference. He had some really bad turnovers. He just didn't play very well," Altman said.
UCLA has been one of the league's most effective teams, but Oregon's defense held them to 45-percent shooting and forced 16 turnovers. Nine came from Anderson.
"There were some possessions that weren't very good. But for us, I thought we made a step," Altman said. "I thought we did a good job getting under Anderson and getting under him." Amardi gave Oregon a three-point lead with a pair of made free throw with 1:14 left, but Jordan Adams converted a three-point play shortly after to knot it. The made basket ended a 14-0 Oregon run.
The Ducks had held a four-game winning streak over UCLA prior to Thursday.
Amardi had 13 points for Oregon.