Brown had 18 kills and 10 digs and McClendon added 16 kills for the Nittany Lions (32-5), who won 19 of their last 20 matches and extended their record number of consecutive national titles.
Penn State won 25-20, 27-25, 25-20. After Katie Slay put down an easy kill to finish the match, she turned her back to the net and welcomed her teammates with open arms as they mobbed her.
The Golden Bears (30-4), who won each of their previous five tournament matches by sweeps, lost 3-0 for the first time since Penn State beat them in last year's regional final. Penn State has beaten Cal four straight years in the postseason, all by sweep.
McClendon, the national freshman of the year, was named the Most Outstanding Player of the final four.
Penn State put itself on the cusp of the title with a hard-fought win in a second set that was tied 16 times.
Cal twice was a point away from winning the set, and tying the match, but couldn't finish.
Ariel Wilson and Kristin Carpenter blocked Adrienne Gehan to tie it 24-all, but Cal setter Carli Lloyd, the national player of the year, answered with a kill to put Cal up 25-24.
Slay and Carpenter blocked Tarah Murrey to tie it 25-25, and consecutive kills by Brown won the set for the Lions.
Penn State took control of the third set after Ariel Scott's kill broke a 12-all tie during an 8-0 run for the Lions.
Cal fought off match point three times before Penn State won it. McClendon looked to have the deciding kill when she hammered a monster drive, but the Bears somehow were able to get the ball back over the net. Slay was there to dunk it and set off the celebration.
Carpenter finished with 46 assists, and Wilson added 12 kills for the Lions.
Murrey had 16 kills, and Lloyd had 33 assists and 11 digs.
The Nittany Lions, who won their fifth title in program history, had new faces in key spots and weren't nearly as dominant as their unbeaten teams of the past two years. Their NCAA-record winning streak ended at 109 in September, and they battled through ups and downs in Big Ten play.
Russ Rose, their 32nd-year coach, said before the tournament that he wouldn't have considered his team to be the favorite. But the Lions again were best at the end.
They dominated Texas in Thursday's semifinals, posting a three-set sweep, and Saturday's victory ran their record NCAA tournament win streak to 24 matches in a row. They won 18 of 19 sets in the tournament.
Penn State's six seniors finished their careers 142-7 and having never finished a season without winning the national championship.
With nine freshman on the roster - national rookie of the year McClendon and blocking star Slay among them - and a sophomore in setter Carpenter, the Nittany Lions are well-positioned to challenge for titles for years to come.
