Stepanek threw some different challenges at the world number one - charging the net on 67 occasions - but Djokovic was still too strong, winning 6-4 6-3 7-5 in two hours 22 minutes.
The contest featured a host of wonderful rallies with both players pushed to the limit and Djokovic admitted it was enjoyable to play in.
Djokovic has looked good in the first week and will play either Sam Querrey or Stanislas Wawrinka in round four.
The first two sets were similar - Stepanek holding his own before Djokovic struck at key times.
The top seed broke through in the 10th game to claim the opener when Stepanek netted a makeable volley and a wonderful backhand pass handed him a 5-3 advantage in the second.
It remained on serve in the third until 5-5 when Stepanek dumped a weak backhand into the net at 15-40.
Eighth seed Janko Tipsarevic won through to a meeting with Nicolas Almagro after prevailing in another five-set thriller.
The Serbian, who was taken all the way by Lukas Lacko on Wednesday, saw off Frenchman Julien Benneteau 3-6 6-4 2-6 6-4 6-3.
Spaniard Almagro, seeded number 10, had a much easier time of it against Jerzy Janowicz, winning 7-6 (7/3) 7-6 (7/4) 6-1.
Kei Nishikori ended the run of Russian Evgeny Donskoy 7-6 (7/3) 6-2 6-3 and awaits the winner of the clash between fourth seed David Ferrer and Cypriot Marcos Baghdatis.
Fernando Verdasco is out, though, going down in five sets to big-serving South African Kevin Anderson.
Anderson will next face fifth seed Tomas Berdych, who enjoyed a routine 6-3 6-2 6-2 win over Jurgen Melzer.
Nishikori will play fourth seed David Ferrer after the Spaniard came through against Marcos Baghdatis 6-4 6-2 6-3.
"It's going to be tough," Ferrer said. "I lost a close game with him at the Olympics. He has good shots with great power."
Venus Williams was unable to stop the Maria Sharapova juggernaut tonight as the Russian powered into the fourth round of the Australian Open.
Sharapova, who won her first two matches in Melbourne without dropping a game, was irresistible as she crushed the seven-time major winner 6-1 6-3 in just 79 minutes on Rod Laver Arena.
It had been expected Williams would provide the second seed with a stiff challenge but she was unable to match her opponent's power off the ground, not to mention her intensity, until the latter stages.
Sharapova said: "I really wanted this victory. I was 5-1 up (in the second set) and made a couple more errors than I would have liked so I was very pleased to have served it out."
The 25-year-old admitted the match was one she had been eagerly anticipating.
"When we both looked at the draw this was the match-up that we were both looking forward to," said Sharapova.
"I was really excited to play Venus again. She is a great athlete and no matter where she is ranked she's always a very tough player to play."
A forehand winner in the opening game handed Sharapova a break and, having staving off the threat of an immediate response, she never looked back.
A further break helped her establish a 4-0 advantage before Williams finally got on the board - ending Sharapova's run of successive games to start the tournament at 28.
It did little to stem the flow of the match, however, as Sharapova marched on, breaking the American's serve for a third time to take the opening set.
She swiftly moved into a 3-0 lead in the second with Williams looking shellshocked.
To her credit, the 32-year-old continued to fight on and she bravely held off three break points in game four, hitting back from 0-40 to take the game with a blistering forehand down the line.
It proved a minor distraction for Sharapova as, despite Williams' best efforts, she broke for 5-1 at the fourth attempt.
She could not serve it out, however, as Williams' pride forced her to break the Sharapova serve for the first time.
But despite some surprising late jitters from Sharapova, the 25th seed could not repeat the feat when the 2008 Melbourne champion served again at 5-3.
Kirsten Flipkens is the next player to stand in Sharapova's way after the Belgian beat Russian qualifier Valeria Savinykh 6-2 4-6 6-3.
Earlier Agnieszka Radwanska, Angelique Kerber and Li Na all moved into round four.
Radwanska eased past British number one Heather Watson, Kerber downed American wild card Madison Keys and Li dropped just five games against Sorana Cirstea.
With all the attention surrounding title favourites Victoria Azarenka, Sharapova and Serena Williams, the chasing pack have gone largely unnoticed but all three were impressive.
Fourth seed Radwanska certainly has momentum behind her - the 6-3 6-1 defeat of Watson was her 12th on the trot in 2013, a run which saw her claim the titles in Auckland and Sydney coming into the season's first grand slam.
"I have played a lot of good matches against top players this year and I must say I am playing well, everything is working," she said.
"I just hope I can keep going. But now it is going to be harder and harder playing against seeded players. We'll see."
German Kerber, the fifth seed, was given some nervy moments by 17-year-old Keys before coming through 6-2 7-5 while Li, a finalist here in 2011, enjoyed a solid 6-4 6-1 win over Romanian Cirstea.
Li will next meet Julia Goerges, who overcame another Chinese player Zheng Jie 6-3 1-6 7-5.
Radwanska will take on Ana Ivanovic, who won the all-Serbian tussle with Jelena Jankovic.
Much has been made of the rivalry between the two but Ivanovic insists it has been overblown.
"Our relationship is fine, it's really good," she said.
"We had a really good week in Prague for the final of the Fed Cup. We were hanging out a lot, joking. It's nice, we have known each other for a while."
Kerber next plays Ekaterina Makarova, who stunned 11th seed Marion Bartoli 6-7 (4/7) 6-3 6-4.
Azarenka and Serena Williams are in action on Saturday, as is Britain's Laura Robson. Robson is third on court two for her match with American Sloane Stephens.
Results from other Australian Open matches
Sania Mirza (IND) /Bob Bryan (USA)  def. Samantha Stosur (AUS)/Luke Saville (AUS) 6-2 6-2
Stanislas Wawrinka (SUI)  def. Sam Querrey (USA)  7(8)-6(6) 7-5 6-4
Daniele Bracciali (ITA)/Lukas Dlouhy (CZE) def. Alex Bolt (AUS)/Greg Jones (AUS) 6-2 7(7)-6(4)
Katarina Srebotnik (SLO)/Nenad Zimonjic (SRB) def. Olivia Rogowska (AUS)/Marinko Matosevic (AUS) 6-3 6-3
Ashleigh Barty (AUS)/Casey Dellacqua (AUS) def. Maria Kirilenko (RUS) /Lisa Raymond (USA)  6-4 6-4
Mike Bryan (USA) /Bob Bryan (USA)  def. Flavio Cipolla (ITA)/Andreas Seppi (ITA)6-3 6-4
Anabel Medina Garrigues (ESP)/Bruno Soares (BRA) def. Bojana Bobusic (AUS)/Chris Guccione (AUS)6-4 6(7)-7(9) -
Su-Wei Hsieh (TPE) /Shuai Peng (CHN)  def. Mathilde Johansson (FRA)/Pauline Parmentier (FRA) 6-2 6-4
Marcel Granollers (ESP) /Marc Lopez (ESP)  def. Paolo Lorenzi (ITA)/Potito Starace (ITA) 7-5 6-4
Jeremy Chardy (FRA)/Lukasz Kubot (POL) def. Samuel Groth (AUS)/Matt Reid (AUS) 6-4 3-6 6-3
Sergiy Stakhovsky (UKR)/Mikhail Youzhny (RUS) def. John Peers (AUS)/John-Patrick Smith (AUS) 6-3 6-3
Aisam-Ul-Haq Qureshi (PAK) /Jean-Julien Rojer (NED)  def. Xavier Malisse (BEL)/Dick Norman (BEL) 7(7)-6(5) 6-4
Eric Butorac (USA)/Paul Hanley (AUS) def. Michael Kohlmann (GER)/Jarkko Nieminen (FIN) 6-1 6-4
Ekaterina Makarova (RUS) /Elena Vesnina (RUS)  def. Mandy Minella (LUX)/Megan Moulton-Levy (USA) 6-4 6-4
Kimiko Date-Krumm (JPN)/Arantxa Parra Santonja (ESP) def. Andrea Hlavackova (CZE) /Lucie Hradecka (CZE)  7-5 3-6 6-3
Liezel Huber (USA) / Maria Jose Martinez Sanchez (ESP)  def. Xinyun Han (CHN)/Yi-Miao Zhou (CHN) 1-6 7(7)-6(3) 6-3
Juan Sebastian Cabal (COL)/Robert Farah (COL) def. Yen-Hsun Lu (TPE)/Go Soeda (JPN) 6-4 6-4
Zi Yan (CHN)/Santiago Gonzalez (MEX) def. Tamira Paszek (AUT)/Alexander Peya (AUT)6-2 6-2
Silvia Soler-Espinosa (ESP)/Carla Suarez Navarro (ESP) def. Dominika Cibulkova (SVK)/Ksenia Pervak (KAZ) 3-2
Sara Errani (ITA) /Roberta Vinci (ITA)  def. Jill Craybas (USA)/Chanelle Scheepers (RSA) 6-2 6-0
Nuria Llagostera Vives (ESP) /Jie Zheng (CHN)  def. Svetlana Kuznetsova (RUS)/Yanina Wickmayer (BEL) 6-3 6-3
Anastasia Pavlyuchenkova (RUS)/Lucie Safarova (CZE) def. Raquel Kops-Jones (USA) /Abigail Spears (USA)  6-4 6-2
Natalie Grandin (RSA) /Vladimira Uhlirova (CZE)  def. Melinda Czink (HUN)/Bojana Jovanovski (SRB) 6-3 6-3