The Bruins will face defending champion Arkansas, which defeated North Carolina 75-68 later Saturday in the other semifinal of the month-long NCAA tournament.
UCLA won 10 national titles from 1964 to 1975 during the coaching reign of John Wooden, but that seemed to mean precious little to Oklahoma State, playing in its first Final Four since 1951.
With 7-footer Bryant "Big Country" Reeves scoring 25 points and hauling down nine rebounds, the Cowboys threatened to win this game until UCLA went on its closing run.
UCLA, led by Tyus Edney's 21 points, Charles O'Bannon's 19 and Ed O'Bannon's 15, led only 64-61 when Oklahoma State's Randy Rutherford threw up an airball on a 3-point attempt with 1:53 left.
The Bruins, which had trailed by three points early in the second half and had seen an eight-point lead virtually vanish after that, finally had the breathing room they needed. UCLA scored the next 10 points on free throws to produce the final score.
Edney sparked the UCLA offense down the stretch with his quick penetrating moves.
"I thought I should be aggressive," he said. "Coach [Jim Harrick] kept screaming, 'Go to the hole.'"
In the second game, after another close finish, Arkansas has a chance at joining Duke as the only repeat champions in the last 22 years.
The Razorbacks, who won their first four games in the NCAA tournament by a total of 15 points, will have a chance to repeat only after surviving a last-minute scare that saw their lead cut to one point by North Carolina. Arkansas got back in the title game behind a great second half by Corliss Williamson and some great defense that held North Carolina to one field goal in the last 15:10.
Williamson, the Most Valuable Player of last year's Final Four, was 9-for-12 from the field in the second half when he scored all but two of his 21 points.
"In the second half, they started getting the ball into Corliss and working their offense," North Carolina coach Dean Smith said.
Arkansas had to survive a hair-raising finish to win. Close games, though, are nothing new to this team, 11-1 in games decided by three points or less.
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In Minneapolis, Connecticut's women's basketball team defeated Tennessee, 70-64, for the national championship Sunday.
The Huskies, at 35-0, became only the second women's team to finish a season undefeated, joining Texas, which went 34-0 in 1986.
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