With the temperatures again sizzling around 33 Celsius (93 Fahrenheit) at Melbourne Park, the American 18-time Grand Slam champion took time to adjust to the hot and humid conditions against the Russian veteran.
She had to save two set points before exploding into action in the second set to easily win 7-5, 6-0 and keep alive her dream of a sixth Australian title.
Djokovic, gunning to be crowned champion a fifth time, was on fire in his showdown against Andrey Kuznetsov, crushing the hapless Russian 6-0, 6-1, 6-4, while defending champion Stan Wawrinka had to work hard to get past Marius Copil.
Williams said she only started finding her range when she relaxed.
"She started out really well, she was really aggressive and I was a little too passive," said Williams, the top seed.
"Once I got down I thought 'Serena, you've done so well here you've got nothing to lose, just have fun and enjoy yourself' -- then I started to play a lot better."
While the old guard of Williams and Maria Sharapova are safely into the third round, the new generation of Eugenie Bouchard and Simona Halep have looked more impressive in the early rounds.
The Pole, a semi-finalist last year, took just 44 minutes to brush aside Sweden's Johanna Larsson 6-0, 6-1 and has only lost four games in two matches.
"She's helped me a lot, on and off the court," Radwanska said of Navratilova. "We're working on a couple of things right now. So far so good."
Williams faces a tricky third round match against another of the new young guns in Spanish world number 24 Garbine Muguruza, who beat Daniela Hantuchova 6-1, 0-6, 6-1.
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