2016 US Open and reached his highest career ranking of three in 2014.
Wawrinka, known for hitting one of the best as well as fastest one handed topspin backhands ever, also won a gold medal in doubles at the Beijing Olympics in 2008.
Wawrinka powered to a one set lead before Rune saved a matchpoint in set two and rallied from a 2-5 deficit to force a decisive set three.
Serving at four games all in the final set, Rune saved breakpoint by striking an ace out wide.
Rune then hit a crosscourt forehand winner to reach gamepoint.
Wawrinka struck a down the line backhand long to lose the game and trail 4-5.
Then serving to stay in the set at 30-0, Wawrinka struck two consecutive crosscourt forehand winners to hold serve and level the set at five games all.
Serving at five games all 40-30, Rune struck a dropshot which Wawrinka ran down and returned with a crosscourt forehand winner to reach deuce.
Rune, who appeared to struggle physically with an injury in the middle and end of the match, stuck a down the line forehand long to face breakpoint.
The Danish player then hit a down the line backhand wide to drop serve and trail 5-6.
Serving for the match, Wawrinka struck one of his signature powerful crosscourt one handed backhand winners to lead 15-0.
Rune, ranked number eight, struck two baseline errors to face matchpoint.
The Danish player then hit a crosscourt forehand long to end the match.
The match was over however the drama wasn't.
The duo had words at the net last November at the Rolex Paris Masters indoor tournament in Paris
following their only prior meeting and the post match handshake at the net this time was frosty as expected
with Rune asking Wawrinka "You got nothing to say now?"
To which Wawarinka replied, "What do you want me to say?"
Yesterday in round four, the Swiss lost to the 11th seeded Jannick Sinner of Italy 6-1, 6-4.
Last year at Roland Garros, the 19 year old Rune posted his best grand slam result to date by reaching the quarterfinals.
The Dane and Swiss will next look to gain valuable rankings points at the Miami Open Presented By Itau in Miami, Florida beginning March 22nd.
