"We just had a most amazing, shocking experience occur in our great city," Glide's founder, the Rev. Cecil Williams, said in a statement. "We are shouting, dancing, rejoicing, and celebrating."
The organization said Friday's winning bidder wanted to remain anonymous. Williams said 10 people engaged in bidding.
Buffett became one of the world's richest men while building Berkshire Hathaway into a conglomerate. But he said most of the questions he gets at the lunches aren't about investing.
As in past auctions, the bids didn't reach astronomical levels until close to the end. Within the final hour, bids jumped from $1 million to the final $3.46 million.
Buffett has supported the San Francisco organization since his late first wife, Susan, introduced him to Williams. Buffett said Williams was a key reason Glide had been able to help so many people after the world gave up on them.
"He's changed thousands of lives that would not have been changed otherwise," Buffett said before the bidding closed.
The previous four winning bids have all exceeded $2 million, with records set every year. Last year's winner, hedge fund manager Ted Weschler, paid $2.6 million.
In fact, Weschler paid nearly $5.3 million to win the 2010 and 2011 auctions, and he wound up getting hired by Buffett last year to help manage Berkshire's investment portfolio. Buffett said he didn't expect to find another new hire through the auction.
Buffett's business brilliance and remarkable record of investment success as Berkshire's chairman and chief executive is a big part of the draw for bidders, though he won't talk about potential investments.
Buffett has also made a mark on the world of philanthropy, so past winners of the lunch have also wanted to discuss giving. Buffett has slowly given away his fortune since 2006, and he plans to eventually divide most of his shares of Berkshire stock among five charitable foundations. The largest chunk will go to the Bill and Melinda Gates Foundation.
Buffett and Gates have also been encouraging other wealthy people to give away at least half of their fortunes. Nearly 80 of the nation's wealthiest families have signed the pledge.
The Glide auction winners traditionally lunch with Buffett at New York's Smith & Wollensky steak house. The restaurant donates at least $10,000 to Glide each year to host the auction lunch.
Winners of the auction have said they believe the time with Buffett was well worth the price they paid. The lunches often continue for several hours as Buffett answers their questions.
Buffett said many of the questions he gets at the lunches are about nonbusiness subjects such as family and philanthropy.