5:33 PM PT -- Kim just posted a photo from her visit, saying, "I had an emotional meeting with Kevin Cooper yesterday at San Quentin's death row. I found him to be thoughtful and honest and I believe he is innocent of the crimes for which he was convicted."

Kim Kardashian was on San Quentin's death row Thursday ... on a mission.

Kim, sporting a noticeably baggy black jumpsuit, took her prison reform efforts on the road to one of America's most notorious prisons ... with the goal of freeing an inmate who has been awaiting death since 1983.

61-year-old Kevin Cooper was convicted of committing 4 heinous murders in Chino Hills, CA in the '80s and sent directly to death row. Between then and now, the death penalty was suspended, reinstated, there was a gas chamber and then death by lethal injection ... and all the while Cooper sat waiting to die, always proclaiming his innocence.

As we reported ... back in October, Kim asked then-Governor of California Jerry Brown to look into Cooper's case because of evidence Cooper has been framed. Brown's ordered DNA testing, in no small part due to Kim's campaign. California's new Governor, Gavin Newsom, ordered additional testing in February.

Newsom's waiting for final DNA test results, but Kim decided to pay a visit so she could have her first face-to-face with the guy she's trying to free. Kim, who wore all black, spent 2 hours with him and is more convinced than ever he was framed.

As for now ... Cooper will not face execution, because Governor Newsom is a death penalty opponent who has suspended all executions while he is in office.

We're guessing Cooper's happy to have KK on his side ... Kim and her legal team have freed 17 inmates gaining freedom over the past few months.