The 88-year-old actress confirmed during Sunday's episode of Watch What Happens Live that she was in the audience when King gave the speech during the March on Washington for Jobs and Freedom in 1963.
"Isn't that amazing?" Moreno asked host Andy Cohen.
"What happened was that Harry Belafonte wanted Dr. King to know that there was people in Hollywood who really meant what they said and loved other people," Moreno said. "He asked him if he could bring some Hollywood people with him."
Moreno said Garner, a white actor, was nervous about how attending the march could affect his career.
"Jim Garner ... came on this with a lump in his stomach. He was so frightened because he was actually afraid he would never work again. But he came," Moreno said.
"I mean, he was drinking Pepto-Bismol all over the place because his ulcer was working up," she added. "But he came, and I've never forgotten him for that."
Moreno said Sunday in an interview with Entertainment Tonight that she was sitting "no more than 15 feet away" from King during the speech. She said King put away his prepared speech and improvised the "I have a dream" portion.
"I still can't talk about it without getting these giant goosebumps," Moreno said. "It was the most extraordinary experience I've ever had. That really activated me. That did it. I thought, with this many people, I'm not alone."
Moreno plays Lydia on the Pop TV series One Day at a Time, which is in the midst of its fourth season. The show will air an animated special Tuesday.