"It fell in my hands and I knew we only had a few seconds left so I put it up," he said.
His putback with 5.3 seconds to go gave UCLA a 70-68 victory over slumping Oregon on Thursday night.
Jordan Adams finished with 19 points for UCLA (17-4, 6-2 Pac-12), which has won five of its last six games to sit at second in the league's standings behind top-ranked Arizona.
Norman Powell added 17.
"It came down to our toughness," Powell said. "We knew that we couldn't give in."
Joseph Young had 25 points for Oregon (14-6, 2-8), which was coming off a 71-44 victory over Washington State that snapped a five-game losing streak, the team's longest since 2011. The string of losses stopped a 13-game winning streak that had Oregon ranked as high as No. 10 in the rankings.
The Ducks have slipped to 10th in the league standings.
"This is not where we want to be, where we thought we'd be," Oregon coach Dana Altman said.
The Bruins were coming off a 76-64 victory at home over California last Sunday.
Norman Powell's fast-break layup and free throw gave UCLA a 62-52 lead its largest of the game to that point with 7:20 left.
Oregon closed the gap with consecutive layups by Jason Calliste and Young to make it 65-62 with 3:21 left. Young added a free throw before Calliste hit a 3-pointer to pull Oregon in front 66-65 with 1:40 left.
Kyle Anderson missed a free throw for UCLA and Tony Parker missed a put-back layup before fouling out. Richard Amardi made both the free throws to make it 68-65 for the Ducks, but Adams hit a layup and added a free throw to tie it at 68 with just under a minute left before Wear hit the winning basket.
Johnathan Loyd missed a jumper for the Ducks as time ran out. After the game, Altman said the plan was for Loyd to drive down the court then kick the ball out to Young for the final shot.
"We knew UCLA would pack it in a little bit inside and not let us get to the rim, so we thought we would have an opportunity to get Joe a clean look," Altman said. "We just didn't get it."
The Bruins and Ducks went into the game as the top two scoring teams in the Pac-12, with Oregon averaging 85.9 and UCLA averaging 84.3.
Wear's jumper gave the Bruins a 13-9 lead in the first half. Oregon pulled into a 17-all tie after Zach LaVine fouled Young beyond the arc and Young made all three of his free throws. Young nailed a 3-pointer off a dish from Dominic Artis to give the Ducks the lead.
Calliste's layup stretched the lead to 27-21 and Oregon led 36-32 at the break. Young led all scorers with 16 points.
A pair of free throws from Norman Powell pulled the Bruins into a tie at 38, before his jumper put UCLA in front. Wear's jumper extended the lead to 45-38.
The Ducks fought back on their distinctive home court, pulling to a 49-all tie on Calliste's layup with 11:17 left in the half.
"We're down, we're up, we're down again," Adams said of the game. "That helps our toughness."
Oregon's Jonathan Loyd played after having surgery on Wednesday to repair a broken nose he sustained in practice on Tuesday. He wore a face mask against the Bruins.
The Ducks were also missing reserve post Arik Armstead, who decided to leave the team to focus on football. Armstead is a defensive end for the Ducks
The Bruins were the first in a stretch that has Oregon playing seven of its next 11 games at Matthew Knight Arena.