Kyrgios overcame a first set code violation to defeat Italy's Marco Cecchinato 7-6 (8/6), 7-6 (8/6), 6-4.
Kvitova a dû sauver une balle de match face à Kovinic, mais elle sera bien au 2è tour: https://t.co/JknGcPyCgX #RG16 pic.twitter.com/NctJToa9In
— Roland-Garros (@rolandgarros) May 22, 2016
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 and needed to make his voice heard.
He then accused umpire Carlos Ramos of "unbelievable bias" for dishing out the violation.
However, Kyrgios recovered his composure to see off world number 124 Cecchinato and set up a second round clash against Dutch lucky loser Igor Sisjling.
French Open: Djokovic set for another crack at elusive title
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.
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.
But she claimed the next three games and goes on to face Taiwan's Su-Wei Hsieh for a place in the last 32.
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.
Meanwhile, defending men's champion Stan Wawrinka insisted Sunday that last year's stunning triumph over world number one Novak Djokovic would have little bearing on his chances this time round.
Roger Federer withdraws from French Open
The 31-year-old Swiss, seeded three this year, only arrived in Paris on Saturday night after clinching his hometown Geneva claycourt 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."
On a low-key day at Roland Garros, Japanese fifth seed Kei Nishikori, a quarter-finalist in 2015, was looking to secure his 50th Grand Slam triumph against Italy's Simone Bolelli.
The two have met twice with Nishikori coming out on top but both encounters - at Wimbledon on 2014 and 2015 - went to five sets.
Also in action are 2014 runner-up and sixth seed Simona Halep against Nao Hibino of Japan while 2009 champion Svetlana Kuznetsova plays Yaroslava Shvedova of Kazakhstan.
This year's Roland Garros is being played with security ramped up in the aftermath of the November terror attacks in Paris.
Storylines of Novak Djokovic, celebrating his 29th birthday Sunday, and chasing an elusive first title or Serena Williams looking to equal Steffi Graf's modern-day record of 22 Grand Slam singles titles were on hold.
The first challenge for organisers was to keep the daily crowds of 30,000 fans safe and sound, a task which was fairly straightforward until last year when another of the city's showpiece sports venues, the Stade de France, was targeted by suicide bombers.
"Security is at the heart of our priorities and it will be reinforced," said Guy Forget, the former player and Davis Cup winner who was appointed as tournament director only in February.
"There will be a double security perimeter with only three entry points. We cannot afford to take the slightest risk."
Metal detectors and sniffer dogs are patrolling the gates while there will be pat-downs and bag searches.
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