The Sound of Music lead, 88, admitted she was a bit intimidated by him before they started filming, as he was "young, fit as can be and really gorgeous to look at."
"I'd never made a movie before, and I'd given birth to my lovely daughter Emma nearly six weeks earlier, and I quickly realized that I had better pull my socks up and get in shape," she quipped. "I found it pretty daunting, I can tell you."
However, her worries quickly subsided, as "Dick could not have been kinder, more genuinely sweet and helpful. I like to think that we did bond instantly."
The Oscar winner remembered how the now 98-year-old was always making her laugh in between takes. "It was so delightful to watch him imitating the animated penguins or attempting to ride the pony from the carousel. Becoming a magical chimney sweep," she shared. "Actually, it was a very happy film for, I think, the entire company."
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Andrews added that she felt "lucky" to have Van Dyke as her costar for her "first venture in Hollywood."
The CBS special also featured comments from the birthday boy himself, who turned 98 on December 13.
He confirmed the British star's words about the fun he had while shooting the flick, explaining of his acting chops, "If I'm not enjoying myself, I’m really bad."
"It’s such a blessing to find a way of making a living that you love, that you’d do for nothing," he shared. "I feel so sorry for people who hate their jobs. I look forward to going to work every morning."
The father-of-four also admitted he's been pretty "lucky" in his career, as he was "lazy" when it came to trying to find new gigs.
"As a businessman, I’m not much good. I would do a movie and come home, and just sit down and wait for the phone to ring," said the movie star. "I wasn’t aggressive. I was out of work a lot because I didn’t go out and look for it."