Belibi dunked early in the fourth quarter, a week after becoming the first woman to do so in a collegiate game since former Baylor star Brittney Griner in 2013. Belibi added seven rebounds.
Freshman Cameron Brink added 10 points and nine rebounds for the Cardinal (7-0, 4-0 Pac-12). Kiana Williams had 10 points and was one of four Stanford players with four assists.
Stanford cruised past its first six opponents, winning by a whopping 48.2 points per game while scoring an average of 93.2 points.
But the Cardinal got tested against the Bruins, who took a one-point lead in the second quarter and didn't trail by double digits until late in the fourth, when Stanford outscored UCLA 18-12.
Michaela Onyenwere scored 19 points and seven rebounds, and Emily Bessoir, a freshman from Germany, added 15 points for the Bruins (5-2, 3-2). They shot just 27% from the floor and were 6 of 28 from 3-point range.
UCLA got to 47-43 in the fourth on a 3-pointer by Lindsey Corsaro. Williams made 1 of 2 free throws before Brink scored six points in a row to extend Stanford's lead to 54-45.
In the second quarter, the Bruins outscored the Cardinal 14-4, including six by Onyenware, to take their first lead of the game, 26-25. The Cardinal regrouped and scored six consecutive points to lead 31-26 at halftime.
Stanford raced to a 21-12 lead in the first quarter, holding UCLA to 23% shooting from the floor.
Stanford: The itinerant Cardinal is headed back to Northern California, having finished off a key stretch. Tara VanDereer became the winningest coach in women's basketball last Tuesday, passing the late Pat Summitt with her 1,099th victory. She picked up two more wins in Los Angeles. The team has held its first seven opponents to 40% field-goal shooting or worse while having four games either postponed or canceled due to COVID-19 concerns. Stanford will spend the holidays in a hotel because of Santa Clara County's order about no contact sports.
UCLA: The Bruins moved back into the Top 10 on Monday. Their only losses so far have come against ranked teams, including by three points to then-No. 7 Arizona.
Stanford: Visits No. 6 Arizona on Jan. 1 in the middle game of a three-game trip.
UCLA: The Bruins are off for nearly two weeks before visiting Oregon State on Jan. 1 in their second Pac-12 road trip. They split their first in Arizona.