Djokovic broke the 34-year-old, 34th-ranked Stepanek late in each set of a 6-4, 6-3, 7-5 win Friday, extending his winning streak to 17 matches at the Australian Open.
In the next match on Rod Laver Arena, Maria Sharapova beat Venus Williams 6-1, 6-3 in an unexpectedly lopsided third-round result.
Williams could consider herself fortunate Sharapova's opponents in her first two matches failed to win a game from the Russian star.
Three matches into this tournament, and Sharapova, who pumped her arms six or seven times after she served out with an ace, has lost just four games heading into her fourth-round match against unseeded Belgian Kirsten Flipkens.
"I think when we both looked at the draw, it was a matchup we were both looking forward to," Sharapova said of Williams, a seven-time major winner. "I was a really determined player out there because I knew the tennis that she's capable of producing and playing. She's a tremendous athlete and a great champion."
Williams didn't feel like a great player on Friday.
"Definitely not my best today, but there's always other days to play better," she said. "I just had a lot of errors (26) ... that never helps."
At Djokovic's post-match news conference, the questions quickly turned from tennis to Armstrong's confessions about doping in cycling during his television interview with Oprah Winfrey in the U.S. Thursday night.
"I think it's a disgrace for the sport to have an athlete like this," said Djokovic, the No. 1-ranked man in tennis. "He cheated the sport. He cheated many people around the world with his career, with his life story."
Djokovic, who has five Grand Slam titles, said the doping program in tennis was sufficient to catch the cheats, though he conceded he hasn't had a blood test that could detect illegal oxygen-boosting agents for six months.
He will play No. 15 Stanislas Wawrinka, who beat American Sam Querrey 7-6 (6), 7-5, 6-4 on Friday, in the fourth round.
Querrey's loss meant that for the second consecutive year, there will be no American men in the fourth round at Melbourne Park. Last year was the first time no U.S. man reached the fourth round at the Australian Open since 1973 when no Americans traveled to the tournament.
During Friday's match, Djokovic was troubled at times against the wily Stepanek, who mixed up the tempo with a lot of serve-and-volley and some unorthodox shot-making.
"Absolutely it was great. Great match and great fun," Djokovic said. "It's always tricky to play Radek. He's a talented player. Skillful player."
Told about the statistics Stepanek won 36 of the 67 points he played at the net Djokovic wasn't surprised at all.
"He's skillful on the net and he was not giving me a lot of rhythm he was changing up the pace on the ball," Djokovic said. "Nowadays everything is based on the baseline. It's nice to see somebody coming to the net."
Stepanek had Djokovic smiling and acknowledging his winners on some points, frustrated him on others with his constant, stay-in-the-point defense, and even had chair umpire Carlos Bernardes grinning with his over-the-shoulder winner to save one match point near the end.
In Friday's last third-round match, fourth-seeded David Ferrer of Spain beat Marcos Baghdatis of Cyprus 6-4, 6-2, 6-3, clinching the 1-hour, 57-minute match with an ace.
Elsewhere, fifth-seeded Tomas Berdych of the Czech Republic beat Austria's Jurgen Melzer 6-3, 6-2, 6-2 and will next play South Africa's Kevin Anderson, who beat No. 22 Fernando Verdasco 4-6, 6-3, 4-6, 7-6 (4), 6-2.
Others advancing included Japan's Kei Nishikori, who will face Ferrer in the fourth round, and No. 8-ranked Janko Tipsarevic, who has a tough next round against No. 10 Nicolas Almagro , a7-6 (3), 7-6 4), 6-1 winner over No. 24 Jerzy Janowicz.
In other women's matches, Angelique Kerber survived some nervous moments before fending off American teenager Madison Keys 6-2, 7-5 in their third-round match, then got to blow out the candles on a cake to celebrate her 25th birthday.
Local organizers brought a cake onto the court for Kerber immediately after the match and the crowd at Rod Laver Arena sang "Happy Birthday." She blew out the candles and said thank you to the crowd and to the 17-year-old Keys.
Kerber will next play No. 19 Ekaterina Makarova of Russia, who advanced after a tough 6-7 (4), 6-3, 6-4 win over 2007 Wimbledon finalist Marion Bartoli. In the fourth round last year, Makarova beat Serena Williams and was the first of only four women to best the powerful American in 2012. Kerber was the last.
Fourth-seeded Angieszka Radwanska, meanwhile, won her 12th match in a row with a 6-3, 6-1 victory over Britain's Heather Watson.
"I'm extremely happy to be playing my best tennis from the beginning of the year," said Radwanska, who won tournaments in Auckland and Sydney earlier this month.
Radwanska will now meet 2008 French Open champion Ana Ivanovic, who beat Jelena Jankovic 7-5, 6-3 in a matchup featuring two Serbians who were both formerly ranked No. 1.
Sixth-seeded Li Na advanced with a 6-4, 6-1 win over No. 27 Sorana Cirstea of Romania and will next play No. 18Julia Goerges, who prevented an all-China fourth-round encounter by beating Zheng Jie 6-3, 1-6, 7-5.
On Saturday, Victoria Azarenka and Serena Williams play their third-round matches and the featured night match has second-seeded Roger Federer taking on resurgent Australian Bernard Tomic, who won his first ATP title last week in Sydney after a poor 2012.