delivering one of the fastest second serveson the tour, struck a 128 miles per hour doublefault to drop serve and trail 1-3.
With Djokovic serving up a break of serve, Rune hit two down the line backhand winners which he followed up a crosscourt forehand passing shot winner to break serve and return the set back on serve at 3-2.
The final set then remained on serve with Djokovic serving at five games all.
Rune struck an overhead winner before Djokovic sent a crosscourt backhand long to reach 30-40.
Djokovic struck an inside out crosscourt forehand wide to drop serve and trail 5-6.
In the final game of the match, Rune saved the first breakpoint he faced in the game by hitting a down the line forehand winner, his 42nd winner of the day to reach deuce.
The Dane then survived seven dueces as well as a time violation warning for taking too much time to start the point by serving.
Djokovic netted a crosscourt backhand while on the run to face matchpoint.
A venture to the net on the following point would prove costly for Djokovic as he netted a forehand half volley to drop the point and the match.
Rune needed 16 minutes to hold serve and finish the match after a total of two hours and 32 minutes.
Rune snapped Djokovic's 13 match winning streak enroute to winning five matches for the week against top ten ranked opponents.
The Dane, who started the year ranked number 103, has won 19 of his last 21 matches.
On Monday, Rune reached a career high singles ranking of ten and is the first alternate at next week's men's professional tour season ending tournament in Turin, Italy.