4:58 PM PT -- A source with direct knowledge of the visit tells us Kim was allowed to go in to visit Rodney as a legal visitation. It's extremely tough to get a visit with an inmate on death row, however, Kim is a legal apprentice so she was able to make it happen.
We're told Kanye wanted to visit Rodney too -- as he was in Houston performing at the jail -- but only legal visitation was permitted. Our sources say the warden knocked on the door to interrupt Kim's visit and let Rodney know the good news ... it was extremely emotional.
4:31 PM PT -- Kim just detailed the meeting, saying, "Today, I had the honor of meeting Rodney Reed in person and the privilege of sitting with him when he got the news that the highest court in Texas had issued a stay of execution and remanded the case back to the trial court for further consideration."
She continued, "Words cannot describe the relief and hope that swept over the room in that moment. That hope had been building over the last few weeks around Rodney's case. We have seen Democrats and Republicans come together. We have seen grassroots activists and lawmakers link arms."
4:31 PM PT -- "We have heard people all around the globe speak up. And all because of a deep belief that every man or woman accused of a crime - especially one punishable by death - deserves the chance to have all available evidence considered."
She finishes, "So grateful for the commitment and passion of everyone who voiced their support, the Texas Board of Pardons and Paroles for their recommendation to issue a 120 day reprieve, and the courts for issuing a stay!"
Kim Kardashian West isn't just lobbying to set a death row inmate free ... she met with him face-to-face with the clock ticking to try to figure out a plan.
We broke the story ... Kim's desperately trying to stay the execution of Rodney Reed -- which was originally scheduled for November 20 -- because she and many others believe there is substantial evidence to exonerate him of the murder he was convicted of more than 20 years ago.
Lucky for both Kim and Rodney, on Friday the Texas Court of Criminal Appeals issued the stay of execution -- recommending a 120-day reprieve.
We're told she wanted the chance to speak with him in person, hear his story and hash out a last-ditch effort to save his life. As we told you, she's publicly pleaded for Governor Greg Abbott to stop the execution.
Rodney is on death row in Livingston, TX for the 1996 murder of Stacey Stites -- where cops initially said he'd raped, assaulted and strangled her to death. Reed has claimed the 2 had a consensual affair, but he's maintained his innocence of killing her for over 20 years now.
Just recently, a former inmate claimed to know the real murderer -- the guy alleges Stites' own fiance confessed to him while behind bars that he killed her for sleeping around.
Along with Kim, lawmakers on both sides of the aisle and countless celebrities have voiced support to stop Reed's upcoming death.