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."