After winning the first set and with the second close Nick Kyrgios entertained himself by starting a debate with the chair umpire about what he thought was a questionable call.
On a big day of tennis in the French capital Nick Kyrgios showed once again that he belongs among the sports elite.
Contesting just his third singles match in 18 months since undergoing shoulder surgery, Kokkinakis went down fighting in a 4-6 6-1 6-4 6-4 loss to eighth seed Kei Nishikori.
The 21-year-old used an injury-protected ranking to gain entry to Roland Garros after falling outside the world's top 1000, but stretched the Japanese superstar for more than three hours in a big morale booster.
Thanasi Kokkinakis lost to Kei Nishikori. Photo: Getty Images
American Keys, the women's No.12 seed, beat Barty 6-3 6-2 for her first win on clay this season. Isner beatt Thompson 6-3 4-6 7-6(5) 6-3.
The losses mean Sam Stosur and Nick Kyrgios are the last remaining Australian hopefuls in the singles draw, with Kyrgios advancing against Philipp Kohschreiber 6-3 7-6 (4) 6-3.
Ash Barty went down to Madison Keys. Photo: Getty Images
Stosur next faces Kirsten Flipkens - a 6-3 6-3 winner over Mandy Minella - for a place in the last 32, after advancing to the second round in Paris for the 11th consecutive year.
Daria Gavrilova, Alja Tomljanovic, Jaimee Fourlis, Bernard Tomic, John Millman and Alex De Minaur had all previously exited Roland Garros.