Djokovic, the 21-time Grand Slam winner, appeared on course for glory after racing to the opening set in just 36 minutes.
But Rune immediately bounced back by breaking the Serbian, 35, early on in the second to take the showpiece to a decider.
The 19-year-old then recovered from an early break in the third set before breaking Djokovic's serve in the 11th game and fending off six break points, to take his maiden Masters title 3-6 6-3 7-5 in two hours and 32 minutes.
Rune, who remarkably survived three match points in his opening match, becomes the youngest Paris Masters champion since Boris Becker, then aged 18, triumphed in 1986.
Rune's victory also ensures he will be the first Danish player ranked in the top 10 in almost half-a-century.
"It means everything to me," said Rune. "It is a perfect way to finish the week and a privilege to share the court with Novak."
Commenting on the final moments of his victory, he added: "It was the most stressful game of my life.
"My heart was almost in my brain, and I was already starting to think about the tie-break. But I am very proud I could finish it. If you told me four weeks ago I would be in the top 10, I would be like, 'what, sorry?', but now I'm here and I'm super proud."
Djokovic said: "I want to say congratulations to you and your team and your family. You absolutely deserve this victory. What an amazing week you have had.
"I am not happy that you beat me, but on the other hand I am happy for you because I like your personality and you are a very dedicated guy who loves tennis and is putting in a lot of hours of hard work.
"It is paying off for you and I am sure the future is bright for you and your team."
Meanwhile, Briton Neal Skupski and Wesley Koolhof, of the Netherlands, secured the season-ending number one spot in the doubles rankings after winning in Paris.
The duo, who have claimed seven titles this year, saw off Ivan Dodig and Austin Krajicek with a comprehensive 7-6 (5) 6-4 victory on Sunday.