Defending men's champion Djokovic withheld temperatures of over 100 degrees on Wednesday to win in straight sets over Leonardo Mayer.
Meanwhile, Williams cruised to victory as the women's top seed over Vesna Dolonc in 63 minutes.
Below are all of the scores along with a recap the highs and lows from the third day of action at the Australian Open.
|Novak Djokovic (2) def. Leonardo Mayer||6-0, 6-4, 6-4|
|Tomas Berdych (7) def. Kenny de Schepper||6-4, 6-1, 6-3|
|David Ferrer (3) def. Adrian Mannarino||7-6, 5-7, 6-0, 6-3|
|Sam Querrey def. Ernests Gulbis (23)||6-2, 6-3, 6-4|
|Stanislas Wawrinka (8) def. Alejandro Falla||6-3, 6-3, 6-7, 6-4|
|Richard Gasquet (9) def. Nikolay Davydenko||7-6, 6-4, 6-4|
|Tommy Robredo (17) def. Julian Benneteau||6-3, 6-7, 6-1, 7-6|
|Jerzy Janowicz (20) def. Pablo Andujar||4-6, 7-6, 7-6, 6-3|
|Fabio Fognini (15) def. Jarkko Nieminen||7-5, 6-4, 3-6, 6-2|
|Jeremy Chardy (29) def. Alexandr Dolgopolov||7-5, 7-6, 6-7, 7-6|
|Kevin Anderson (19) def. Dominic Thiem||6-4, 6-3, 6-4|
|Florian Mayer def. Mikhail Youzhny (14)||6-4, 3-6, 6-3, 3-6, 6-3|
|Denis Istomin def. Dmitry Tursunov (30)||7-6, 4-6, 6-1, 6-4|
|Damir Dzumhur def. Ivan Dodig (32)||4-6, 4-6, 6-3, 4-1, ret.|
|Edouard Roger-Vasselin def. Guillermo Garcia-Lopez||7-6, 6-4, 4-6, 6-1|
|Vasek Pospisil def. Matthew Ebden||3-6 7-6 7-6 6-1|
|Li Na (4) def. Belinda Bencic||6-0, 7-6|
|Serena Williams (1) def. Vesna Dolonc||6-1, 6-2|
|Samantha Stosur (17) def. Tsvetana Pironkova||6-2, 6-0|
|Casey Dellacqua def. Kirsten Flipkens (18)||6-3, 6-0|
|Monica Niculescu def. Sabine Lisicki (15)||2-6, 6-2, 6-2|
|Flavia Pennetta (28) def. Monica Puig||6-3, 6-4|
|Angelique Kerber (9) def. Alla Kudryavtseva||6-4, 6-2|
|Eugenie Bouchard (30) def. Virginie Razzano||6-2, 7-6|
|Ana Ivanovic (14) def. Annika Beck||6-1, 6-2|
|Ekaterina Makarova (22) def. Irina Falconi||6-2, 7-5|
|Alison Riske def. Yanina Wickmayer||6-1, 6-1|
|Mona Barthel def. Luksika Kumkhum||4-6, 6-3, 6-4|
|Lauren Davis def. Julia Goerges||7-5, 2-6, 6-4|
|Jie Zheng def. Madison Keys||7-6, 1-6, 7-5|
|Daniela Hantuchova (31) def. Karolina Pliskova||3-6, 6-3, 10-12|
|Lucie Safarova (26) def. Lucie Hradecka||6-7, 6-3, 6-0|
Djokovic, seeded second in the men's singles draw, advanced, 6-0, 6-4, 6-4, after employing a serve-and-volley game designed to get him out of the heat as soon as possible.
He completed a dominant first set in just 22 minutes despite taking a tumble and soon thereafter extended his excellent record in Melbourne:
Mayer was thoroughly outclassed by Djokovic and made 39 unforced errors as the Serb won his 23rd straight match at the Australian Open. It was Djokovic's 26th consecutive victory overall, dating back to the 2013 U.S. Open.
Much like Djokovic, Williams was keen to complete her second-round match quickly and dispatched 24-year-old Dolonc, 6-1, 6-2.
Having won this tournament on five previous occasions, Williams has not had a title victory at Melbourne since 2010, buts she is playing with the desire and focus of a woman on a mission.
The match was decided at the service line, where Williams hit in 66 percent of her first serves and won 85 percent of those points against Dolonc, who made eight double faults.
In the men's singles, third-seeded David Ferrer progressed to the third round after beating Adrian Mannarino of France in four sets while eighth seed Stanislas Wawrinka won over Alejandro Falla, also in four sets.
In the women's draw Li Na, seeded fourth, was victorious over Belinda Benci, while Sabine Lisicki—twice a runner-up at Wimbledon, most recently in 2013—crashed out against Monica Niculescu.
Heat was again a major factor with Croatian Ivan Dodig opting to retire in his men's singles game against Damir Dzumhur because of the conditions.
Dodig, who withdrew two hours and 22 minutes into his match, claimed that he feared for his life, according to Simon Briggs of The Telegraph:
"Today, 30 minutes after the match I could not walk," Dodig said. "There was 10 people around me. I was thinking I could maybe even die here."
BBC Sport reported that Williams claimed the heat had affected her sleep. Temperatures are expected to rise again ahead of play on Thursday and Friday.