Jane, who plays Sue Sylvester on the hit musical series, appeared on America's The Tonight Show and described Cory as a "bright light" who didn't leave "one day unlived".
The actress was already booked to appear on the programme before Cory passed away on 13 July, and host Jay Leno commended her for not cancelling.
He then asked Jane to tell him about her friend and, with her voice cracking slightly, she said: "Cory had one of the biggest hearts.
"[He] was a real bright light and was one of those guys that, you know, he knew he was breathing rarified air, the gifts that this wonderful show gave us.
"He was always aware that it was a gift and he was quite generous. He was one of those adventurous types of those people.
"I always admired how he would get up…you know, he would fly to Mexico, he'd throw parties for his friends. I don't think he left one day unlived.
"He was a real bright light in our family and we've lost a really great guy."
Jay then asked Jane how she would like Cory to be remembered.
While taking deep breaths, she replied: "He once flew across the country on his own nickel to meet with a sick kid whose last wish was to meet him.
"That's just the kind of guy he was...just a real giver."
Earlier this week, a coroner confirmed that Cory had died alone in his hotel room from a heroin and alcohol overdose following a night out with friends in Vancouver, Canada.
Cory's girlfriend and fellow Glee star Lea Michele has since released a statement thanking her family, friends and fans for their "love" during this devastating time.
Lea's rep added that she has been "grieving alongside his family" following their "profound loss" and asked that their privacy is respected.
Watch Jane's touching tribute to Cory below: