Vidal and his partner Howard Austen were on holiday in Ravello in the summer of 1984, when the Dead Man Walking star, who was in town shooting a movie, discovered she was pregnant with her then-boyfriend Franco Amurri's child.
She tells Vanity Fair magazine, "Gore always says Eva was conceived at Ravello. I was staying with them (Vidal and Austen) and bought the (pregnancy) kit in town, so he and Howard were the first to know the test was positive."
Sarandon remained in Europe after becoming a first-time mum the following March (85), and the Oscar winner reveals Vidal was always there to lend a hand.
She explains, "After Eva was born, I was in Ravello with her. I was nursing, and she had these terrible allergies. It was so difficult for me and for her, but Gore and Howard were such a comfort!"
The pair's relationship continued to grow over the years, with Vidal later becoming the godfather to her second child with actor Tim Robbins, Miles Guthrie.
The playwright passed away last summer (Jul12) and Sarandon insists she will also remember him as a great friend: "The most amazing thing about Gore is that he... (had) the world's biggest heart... (and) always had my back."