The Bruins (21-1-3) won the tiebreaker 4-2 to advance to face Florida State (23-1-3) on Sunday in the championship game. The Seminoles beat Virginia Tech 3-2 in the first semifinal.
"I just give a lot of credit to the UCLA girls for really rising to the occasion," Bruins coach Amanda Cromwell said. "We've been through it. We've been tried and tested. I'm just really proud of the team right now."
Katelyn Rowland stopped two of Virginia's four attempts in the shootout.
The Bruins rallied to force overtime with Ally Courtnall's goal in the 85th minute. Makenzy Doniak scored in the 73rd minute for the Cavaliers (24-1-1), the tournament's overall No. 1 seed.
Each team converted its first two penalty kicks before Lauren Kaskie gave the Bruins a 3-2 advantage. Rowland then stopped a shot by Alexis Shaffer.
After Virginia's Jessie Ferrari saved a shot by Kodi Lavrusky, Rowland stopped a shot by Morgan Brian to set the stage for White's winning kick.
"Being the last one to take a PK, there was a lot of pressure on that one, obviously," White said. "But I was just trying not to overthink it and put it where I wanted to, and it worked out."
Ferrari, who had played in one game all season, replaced starting goalkeeper Morgan Stearns for the shootout.
"We've been practicing these all year," Virginia coach Steve Swanson said. "We have confidence in all of our goalies, but in that situation Jessie has proven to be very capable. We're confident in her. It's not something that we just made a decision on randomly. It's something we've been working on. We knew that if it got to that situation that we were going to do that."
UCLA extended its unbeaten streak to 20 games en route to reaching the NCAA final for the fourth time overall and the first since 2005.
Virginia appeared to be on its way to its first NCAA final when Doniak took advantage of a rare mistake by UCLA's top-ranked defense.
UCLA defender Abby Dahlkemper attempted to clear the ball by passing it back to Rowland, but Dahlkemper did not make solid contact on the ball with her foot. Doniak, who already was running toward the goal, kept sprinting and reached the ball before Rowland. She juked past Rowland with a dribble to the right and kicked the ball into the middle of the empty net.
"It's hard to dig out of that kind of mistake sometimes, but we just kept pushing and fighting and scrapping," Cromwell said. "That's what really has set the tone for the season."
UCLA tied it when Courtnall slipped behind part of Virginia's defense unmarked. Sarah Killion threaded a pass into the box to Courtnall, who ripped a ground-hugging shot past Stearns.
"She kind of came out of the blind spot," Stearns said.
The Bruins dominated play after a first half that featured no shots on goal between the teams. UCLA generated the best scoring opportunities in the second half, one of which Stearns saved with a diving punch.
The same was true of the overtime periods, where the Bruins twice hit the post with shots as they peppered Stearns. Courtnall lofted a shot midway through the second overtime that hit the post, bounced off Stearns, and hit the post again.