The interview began with the "Happy Days" alum greeting Barrymore, expressing his desire to be in-studio in order to give her a hug, which she echoed.
"I wish I was there to give you a hug because when I met you when I was young, you actually changed my life forever because The Fonze -- the most important man on the planet -- was nice," she recalled. "I was like, 'Then everybody has to be nice because The Fonze is nice.'"
The "50 First Dates" star continued: "I would clock the way you treated people and there was something about your kindness that made me know that that was the marching order of life."
Winkler then expressed his gratitude for the praise.
"That is one of the most wonderful compliments I've ever gotten," he said. "I never think of being nice, I think of being grateful. I think that I am so happy that I get to do what I dreamt of doing and it has grown over the years."
The star then explained that he "got The Fonze" on his 27th birthday, which was eventually followed by landing his Emmy-winning role on "Barry" on his 72nd birthday.
"In a very few days, I'm going to be 75 which is really hard to say," he continued. "Because inside you don't feel it, but my knees, my knees are 75."
Barrymore then joked that her "lower back is 89."
"It's true, you get older and your number starts going up and then what you thought seemed like an older number doesn't," she added.
Winkler then discussed his career as an author, which began when his agent suggested he write a children's book about his own struggles with dyslexia. He's since written a plethora of books.
He didn't learn of his own disability, however, until his step-son was tested for a learning disability.
"My oldest son Jed -- my step-son who came as a beautiful gift with the marriage -- we had him tested in the third grade and everything they said about his, was true about me," the actor shared. "And I realized I wasn't stupid ... I realized I had something with a name."
Finally, Winkler recounted one of his earliest experiences in Hollywood after relocating from New York.
"The first time, when I came from New York to Hollywood, the first job I had, I had four lines on 'The Mary Tyler Moore Show,' which was the 'Friends' of its time," he recalled. "They said, 'Lunch,' and all these big stars, they all went to lunch, and I just was in the middle of the soundstage and I had no idea where to go, no one had told me. I felt really alone."
He concluded: "I swore I would never let anybody on a set I was on feel that way ever again. No matter what show I do, if there is a guest, I take that guest, man or woman, by the hand and show them where they can get anything done during the day.