The Cardinal grabbed a 23-6 lead on Tinkle's layup. Tinkle accounted for 10 points in the first 10 minutes of the game.
Ogwumike, the reigning Pac-12 women's player of the week, converted a layup to make it 31-11. But the Ducks responded with a 12-2 run, capped by Ariel Thomas' 3-pointer that trimmed Stanford's lead to 33-23 with 3:43 left in the half.
Stanford led 38-27 at the break, and extended its advantage to 51-29 on a 3-pointer from Toni Kokenis. Sara James' 3 made it 71-45 with 6:10 left in the game.
Oregon shot just 28.4 percent for the game.
"At the end of the day, you can't shoot in the 25 to 28 percent range and expect to win," Westhead said.
Ogwumike came into the game ranked sixth in the nation with an average of 22 points, and seventh with an average of 12 rebounds. Her double-double against Oregon was her 16th this season.
Alleyne leads the conference and is ranked 3rd in the nation with an average of 12.9 rebounds per game. She is the first freshman to lead the league in rebounding since Arizona's Shawntinice Polk in 2002-03.
"I'm working hard to get to No. 1 in the nation," Alleyne said.
The Ducks have struggled with injuries, and were even down to a seven-player rotation at one point earlier in the season. But they got a boost when Liz Brenner returned after missing most of the nonconference schedule while she helped Oregon's volleyball team reach the NCAA championship game.
The Ducks, sitting in last place in the conference, broke through for their first Pac-12 victory last week at Washington State. Oregon's only other wins came in nonconference play against Fresno State and Samford.
Westhead, who has coached in the NBA, WNBA and for men's and women's teams at the college level, praised VanDerveer and her team.
"I have the highest regard for her team and the way she presents them," he said. "Couldn't be much better."