Djokovic, whose last defeat came against Rafael Nadal in the U.S. Open final in September, is aiming to be the first player to win four Australian Open titles in a row in the Open Era.
And he is looking the part, despite being broken in his first attempt to clinch the match against Istomin.
He has won all three matches so far in straight sets and his major threats — top-seeded Nadal, Wimbledon champion Andy Murray and 17-time Grand Slam singles champion Roger Federer — are in the other half of the draw.
"I have to be satisfied ... as the tournament progresses I'm playing better and better," Djokovic said. "It's important not to underestimate any opponent. Having the right approach to the court, having the right intensity, starting from the first point to try to show to your opponent that you're there to win."
Montreal's Eugenie Bouchard, the No. 30 seed, reached the fourth round of a Grand Slam for the first time on Friday as she beat American Lauren Davis 6-2, 6-2.
Before rain cooled things off at Melbourne Park, Serena Williams persevered through a fourth day of searing temperatures to also advance.
Five-time champion Williams equaled Margaret Court's Australian Open mark of 60 match wins with her second-round victory, and beat that in the third round when she also matched Lindsay Davenport's record of 69 main-draw matches here in the Open era.
On Sunday, she'll play former No. 1-ranked Ana Ivanovic, who beat 2011 U.S. Open champion Sam Stosur 6-7 (8), 6-4, 6-2.
Williams withdrew from the doubles with her sister Venus, avoiding any extra exposure to the blazing sun during the once-in-a-century heat wave that had gripped Melbourne for nearly all of the first week.
The temperature hit 39 Celsius (102 Fahrenheit) during Williams' match and topped 42 C (108 F) by the mid-afternoon, but humidity remained low and there was no reason for organizers to invoke the Extreme Heat Policy and suspend matches for the second day in a row.
It dipped to 32 C (90 F) before the night matches as a cool change kicked in, and continued to drop before play ended Friday. The forecast for the weekend and most of next week was for cool and cloudy conditions.
Williams has won 24 matches dating back to August, carrying momentum from her dominating 2013 into a new season. She won 78 of her 82 matches and won 11 titles last year, and seems to be getting better with age.
"I feel like, in life 32 is young. In sports it's old," she said. "But for whatever reason, I feel like I just never was really able to reach my full potential, and I feel like recently I just have been able to do a little better. I just keep trying to improve on everything."
In earlier women's play, Li Na, a two-time finalist here and a major threat to top-ranked Williams in the top half of the women's draw, had to save a match point before coming back to beat No. 26-seeded Lucie Safarova 1-6, 7-6 (2), 6-3 in 2 hours, 37 minutes.
No. 9 Angelique Kerber advanced earlier with a 6-3, 6-4 win over American Alison Riske, and said her main aim had been to "get off the court before it became really hot."
No. 22 Ekaterina Makarova advanced with a 6-4, 6-4 win over Monica Niculescu and No. 30 Eugenie Bouchard beat American Lauren Davis 6-2, 6-2 to set up a fourth-round match against Australian wild-card entry Casey Dellacqua, who beat 2010 semifinalist Zheng Jie of China 6-2, 6-4.
In night men's matches, No. 15 Fabio Fognini beat American Sam Querrey 7-5, 6-4, 6-4 and will play Djokovic on Sunday in the fourth round. No. 17 Tommy Robredo defeated No. 9 Richard Gasquet 2-6, 7-5, 6-4, 7-6 (6) and to set up a fourth-round match against a well rested Stanislas Warwinka.
Wawrinka received a walkover Friday when Vancouver's Vasek Pospisil withdrew with a back injury, giving him three full days off before his match against Robredo.
Third-seeded David Ferrer beat No. 29 Jeremy Chardy 6-2, 7-6 (5), 6-2 and next plays Florian Mayer, who beat No. 20 Jerzy Janowicz 7-5, 6-2, 6-2.
No. 7 Tomas Berdych beat Bosnian qualifier Damir Dzumhur 6-4, 6-2, 6-2 to set up a Sunday clash with No. 19 Kevin Anderson, who beat Edouard Roger-Vasselin 3-6, 4-6, 6-3, 7-6 (5), 7-5.