"It's about friendship, a very special friendship," said Torre, who talked about the night in 1962 when, as a young catcher for the Milwaukee Braves, he stayed up all night talking baseball with the Dodger legend.
"We both missed curfew," recalled Koufax.
"Yes, we did," said Torre. "Yet the next day I was playing and you were sitting on the bench watching the game wearing your slippers."
The sellout audience of 7,100 roared with approval.
"This is like a teenager or a baby getting his choice of presents at Christmas," said Koufax's former Dodger teammate Lou Johnson before the event. "Having Sandy come back in this environment tonight brings back a lot of memories. It's just awesome. He has a presence about him that is just like ... the Pope."
"I've been in love with him since I was 9 years old," said Cindy Inez of Palmdale, Calif. "I got a ball that he pitched with that he signed for me a few years back and I am hoping, maybe tonight, I may get to meet him again."
Inez then rolled up the left arm of her Dodger jacket to show off the blue Dodgers script and Koufax's No. 32 in red, tattooed on her left forearm.
"I just made up my mind one day that I wanted a tattoo, something with Sandy, to stay with me forever," said Inez. "My family thinks I'm crazy. I don't care. They know how much I love Sandy and they're fine with it."
The evening was moderated by Los Angeles Times sports columnist T.J. Simers, who shuffled questions between the two baseball legends. Some were baseball related, and others were personal, like having Torre recite the names of his wife Ali's 15 brothers and sisters. The skipper stumbled through eight of her brothers and tried to get the other names in before the evening ended.
As for Koufax, Simers tried to have the low-key legend explain if he really is as reclusive as the media has made him out to be.
"I don't know if I dropped out of sight," said Koufax. "I go to the Final Four every year, with 45,000 other people. I go to golf tournaments and walk around if I have a friend playing in it. I go to the Super Bowl occasionally. I go to Dodger Stadium. I worked for the Dodgers for almost 20 years."
Simers had Koufax clear up many of the myths about him, and the former pitcher said almost every one was fictional.
Simers finally asked if it bugged Koufax that people perceived him as "soft."
"Oh ... no," said Koufax. "That didn't bug me at all."
"Then what did bug you?" asked Simers.
"Sportswriters like you," replied Koufax to a thunderous ovation.
Torre told the crowd that Derek Jeter was the greatest player who ever played for him, and that he was first offered the Yankees' general manager job in 1996. He also said he was the fourth choice to be the club's manager, behind Tony La Russa, Davey Johnson and Sparky Anderson.
"Davey Johnson had already committed to Baltimore," recalls Torre. "Tony La Russa took over for me in St. Louis, where I was fired, and Sparky didn't want to come east. And there I was, the great choice.
"This was the greatest opportunity I had ever had. I've got nothing to lose. I had a great time and I knew I was going to find out if I could manage."
Throughout the evening, which would raise $750,000 for Torre's foundation, one thing was evident -- Torre and Koufax have a deep affection for one another.
"This man has been very special to me," said the Dodger manager about his old friend. "We have never been teammates. We played together on All-Star teams, but my first World Series, in 1996, when I walked into my office at Yankee Stadium, his was the first message on top, wishing me luck.
"When I was diagnosed with prostate cancer, he was just about the first guy who called me. When I got off the plane after saying goodbye to the Yankees, he was the first guy to call. It has been a very special relationship and one that we don't have to talk to each other every day.
"It's something that I treasure, and I'm so touched, and my wife, Ali, is very touched, and our foundation certainly thanks you for being here."
With that, the two friends for almost 50 years walked off the stage together to yet another thunderous ovation.
Ben Platt is a national correspondent for MLB.com. This story was not subject to the approval of Major League Baseball or its clubs.