The actress, 61, took to Instagram on Friday with a touching tribute to the late Hollywood icon, who died Wednesday at the age of 103. Douglas starred in "The Vikings" in 1958 alongside her parents, Tony Curtis and Janet Leigh.
The "Knives Out" actress stressed that Douglas was an "important" person in her parents' lives, but also shared how she may not be alive if it wasn't for the actor.
"I just remembered this morning that Kirk saved my life when I rode my tricycle into the pool at a party and he dove in and brought me up from the bottom, still peddling," Curtis wrote, captioning a throwback black-and-white photo of Douglas with her parents.
Curtis also revealed how the families dealt with similar tragedies and leaned on one another in times of grief.
"I was in school with their son, Eric who they lost in 2004. Tony lost his son, Nicholas in 1994. Families tied together in life and success and loss and struggle, past and present. Kirk is an example for us ALL," she continued.
"It is with tremendous sadness that my brothers and I announce that Kirk Douglas left us today at the age of 103," Michael Douglas wrote Wednesday. "To the world he was a legend, an actor from the golden age of movies who lived well into his golden years, a humanitarian whose commitment to justice and the causes he believed in set a standard for all of us to aspire to.
"But to me and my brothers Joel and Peter he was simply Dad, to Catherine, a wonderful father-in-law, to his grandchildren and great grandchild their loving grandfather, and to his wife Anne, a wonderful husband."
Michael concluded: "Kirk's life was well lived, and he leaves a legacy in film that will endure for generations to come, and a history as a renowned philanthropist who worked to aid the public and bring peace to the planet. Let me end with the words I told him on his last birthday and which will always remain true. Dad -- I love you so much and I am so proud to be your son."