Kyrgios overcame a first-set code violation to defeat Italy's Marco Cecchinato 7-6 (8/6), 7-6 (8/6), 6-4.
The 17th seed picked up the warning for screaming at a ball boy on a shivering Court One where the temperature refused to budge above 15 degrees.
Kyrgios insisted he only screamed at the youngster during the first-set tiebreak because he wanted his towel.
He then accused umpire Carlos Ramos of "unbelievable bias" for dishing out the violation.
"All of us in this room know that if that was me, it would have been a circus. The fact that nothing happened (to Djokovic) speaks for itself," said Kyrgios who ranted on court that Ramos's decision was "fucking bullshit".
The code violation out on Court One was handed down when Kyrgios screamed "towel" at the ballboy.
"When I get my towel I always say thank-you to the ballboys but sometimes you get mad at them," added Kyrgios.
The 21-year-old Australian fired 16 aces and 50 winners on his way to victory as he attempts to go beyond his best performance in Paris -- a third-round exit to Andy Murray 12 months ago.
Kyrgios's latest brush with the authorities came on a day when heavy rain brought a suspension of action after just four hours of play.
In that time, only nine of the scheduled 32 singles matches had been completed.
- Kvitova survives -
Czech 10th seed Kvitova survived a scare to beat Danka Kovinic of Montenegro 6-2, 4-6, 7-5.
The two-time Wimbledon champion was two points away from defeat when she trailed the world number 57 at 4-5 in the decider.
Kvitova, a semi-finalist in Paris in 2012, committed 10
double faults in a typically rollercoaster display against an opponent who made the Istanbul final on clay this season.
Hsieh made the second round by beating Spain's Lara Arruabarrena 7-6 (8/6), 6-3.
There were also wins for Russian 24th seed Anastasia Pavlyuchenkova and Swiss qualifier Viktorija Golubic.
Benoit Paire, the French 19th seed, gave the hosts a winning start with a 6-2, 4-6, 6-4, 1-6, 6-4 victory over Moldovan qualifier Radu Albot.
The 31-year-old Swiss, seeded three this year, only arrived in Paris on Saturday night after clinching his hometown Geneva clay-court title.
"I watched some highlights of the final. I never watched it completely," said Wawrinka, who starts his campaign on Monday against Lukas Rosol, the Czech player he defeated in the Geneva semi-finals on Friday.
"But it was one year ago. It's a completely different story.
"I'm playing good tennis. It was good to win the trophy yesterday. It gives me a lot of confidence and happiness. I'm excited to start tomorrow."
He was comfortably placed at 6-1, 5-4 ahead.
Lucie Safarova, the Czech 11th seed who was runner-up to Serena Williams last year, was cruising against Vitalia Diatchenko, 6-0, 1-0.
Russian world number 223 Diatchenko is playing her first match since injuring her left foot at the US Open last year.
