California (22-9), a Final Four team last season, held on when Erin Rooney's final shot for the Rams came up short.
There were eight ties and nine lead changes in the second half, with the lead going back-and-forth three times in the closing minute.
Afure Jemerigbe was fouled on a drive for Cal with 31 seconds left, and made both free throws for a 62-61 lead for the No. 7 seed in the Notre Dame Regional.
After Rooney drove for a layup against Boyd with 19 seconds left, Boyd responded with a jumper at the other end before the Rams called timeout to set up a final play for Rooney.
Rooney finished with 17 points, 10 rebounds and five assists for Fordham (25-8), the Atlantic 10 tournament champ playing in its first NCAA tourney in 20 years. The Rams are only six years removed from an 0-29 season but now have consecutive 25-win seasons under coach third-year coach Stephanie Gaitley.
Boyd also had 10 assists and six rebounds for the Golden Bears, who play No. 2 seed Baylor Monday night at 6 p.m. PT.
Jemerigbe, along with Boyd a returning starter from Cal's national semifinal loss to Louisville last April, added 13 points for Cal. Reshanda Gray had 10 points and eight rebounds.
It was only appropriate Boyd and Rooney seemed to have such an impact and were involved so much together in the game. They were among the three players in the country who entered the NCAA tournament averaging 14 points, six rebounds and five assists a game.
Cal, which trailed by as many as seven points before halftime, got even at 39 about 3 minutes into the second half when Boyd stole the ball from Rooney.
Boyd drove for a layup and was fouled by Rooney, whose left foot slipped awkwardly while trying to make a defensive stop. Rooney left the game only momentarily and Boyd made the free throw to make it 39-all.
After the Golden Bears came up on empty on a possession when they had six shots with about 6 minutes left, Rooney made a 3-pointer over Boyd to put the Rams up 54-52. The game was quickly tied when Jemerigbe had a putback on Boyd's missed 3-pointer.
Cal coach Lindsay Gottlieb, whose 79 wins in her first three seasons are the most by any Cal coach in a three-year span, grew up 25 miles north of Fordham. She watched the Rams play and even went to camps on the Bronx campus as a kid.
Any other time, Gottlieb would have been pulling for the Rams. This time, she's glad Cal isn't the team headed home.