Williams has won the Australian Open six times
Defending women's champion Serena Williams reached the second round of the Australian Open with a tense 6-4 7-5 win over Italian Camila Giorgi in her first tour match in four months.
The American, 34, had been struggling with a left knee injury in the build-up, but came through unscathed.
Men's champion Novak Djokovic went through in straight sets, beating South Korea's Hyeon Chung 6-3 6-2 6-4.
Roger Federer and Maria Sharapova also won easily in Melbourne on Monday.
Third seed Federer beat Georgian Nikoloz Basilashvili 6-2 6-1 6-2 in 72 minutes while fifth seed Sharapova needed just one minute longer to see off Nao Hibino of Japan 6-1 6-3.
Players struggled as temperatures reached 34C but the main talking point was a report by the BBC and BuzzFeed News which said 16 top-50 players over the past decade, including Grand Slam doubles champions, had repeatedly been suspected of match-fixing without facing action.
Association of Tennis Professionals (ATP) chief Chris Kermode rejected any suggestion that match-fixing evidence had been covered up or ignored.
"The Tennis Integrity Unit and the tennis authorities absolutely reject any suggestion that evidence of match-fixing has been suppressed for any reason or isn't being thoroughly investigated," Kermode told reporters.
"And while the BBC and BuzzFeed reports mainly refer to events from about 10 years ago, we will investigate any new information, and we always do."
Williams had not played a competitive match since the US Open in September, but she made light of her preparation problems as she edged past world number 34 Giorgi.
"It's great," the world number one said when asked about the knee injury that forced her to pull out of the Hopman Cup. "It was an hour and 43 minutes and I didn't feel it at all."
The top seed believes her extended rest stands her in good stead as she chases a 22nd Grand Slam singles title.
"I just needed a break," she said. "I have been going non-stop since the Olympics in London, and seeing that this is another Olympic year, I wanted to start the year out really fresh and really go at it again as hard as I can."
Djokovic beat Britain's Andy Murray in the 2015 final
Djokovic is bidding to equal Australian Roy Emerson's record of six Australian Open crowns.
The Serbian top seed, who won three of the four Grand Slams last year, outclassed his teenage opponent, hitting 40 winners to Hyeon's 16.
"It's an absolute pleasure to come back to Rod Laver Arena, it's the most successful court in my career and there have been many memorable moments in the matches I've played here," Djokovic said.
Kvitova wrapped up victory in 70 minutes as temperatures proved a challenge
Sixth seed Petra Kvitova was the first player to win a match, beating Thailand's Luksika Kumkhum 6-3 6-1.
The two-time Wimbledon champion, who lost to the Thai in the first round in 2014, was playing her first match of the year after a stomach virus forced her to pull out of two warm-up events.
"Now I can breathe a little bit normally," the Czech said. "I got really nervous before the match. I didn't sleep well actually. The memories from two years ago were a little bit difficult.
"I had an interrupted lead-up and lost some weight but I'm feeling much better now."
American wildcard Noah Rubin, ranked 328th in the world, caused the shock of the day by knocking out 17th seed Benoit Paire.
The 19-year-old earned his first Grand Slam victory with a 7-6 (7-4) 7-6 (8-6) 7-6 (7-5) success against the Frenchman.
"My girlfriend's sending me pictures - I'm trending on Twitter. I mean, that stuff is cool," he said.
"But people have done way better than me at my age. People have won Slams at my age so winning one round is not too terrific."
Former world number one Caroline Wozniacki, the 16th seed from Denmark, was knocked out 1-6 7-6 (7-3) 6-4 by world number 76 Yulia Putintseva of Kazakhstan.
"I was cramping the whole third set. I tried to keep my emotions inside and imagine that I was losing," Putintseva, 21, said.
"I would say it's a pretty rubbish start to the season. It wasn't a pretty first set but I got it done and really should have closed it off in two," Wozniacki said.
Putintseva triumphed after three hours and three minutes
Italy's Sara Errani, the 17th seed, had injury problems and became the first women's seed knocked out, losing 1-6 7-5 6-1 to 21-year-old Russian Margarita Gasparyan.
The 24th seed, Sloane Stephens, who beat Serena Williams in the 2013 Australian Open quarter-finals, went out 6-3 6-3 to Chinese qualifier Wang Qiang.
Big-serving Croat Ivo Karlovic became the first player to retire on court during the tournament, the 22nd seed pulling out of his contest with Federico Delbonis on Court 14 in the third set while trailing 7-6 (7-4) 6-4 2-1.
Errani receives treatment during her match
Czech sixth seed Tomas Berdych and Japan's seventh seed Kei Nishikoribreezed into the second round with straight-set wins, while Australia's Nick Kyrgios beat Pablo Carreno Busta of Spain 6-2 7-5 6-2.
"The home crowd is a massive advantage for me," said 20-year-old Kyrgios.
"I think knowing they are behind you when you're feeling physically tired or mentally drained, they give you the spark you need."
French ninth seed Jo-Wilfried Tsonga needed four sets to beat Marcos Baghdatis of Cyprus.
In the women's draw, fourth seed Agnieszka Radwanska of Poland showed no signs of her recent leg injury in overcoming Christina McHale 6-2 6-3.