Although the world No 1 came through the encounter against the 31st seed with a 6-4 6-3 7-5 victory, Stepanek made him scrap for every point.
However Djokovic, who is aiming to become the first man to with three successive titles in Melbourne in the Open era, had enough to break Stepanek's resistance.
"It was a great match and great fun. It's always tricky to play Radek, he's a very talented player," Djokovic said.
"He's very skilful on the net and he made a lot of great first volleys, making me always play an extra ball. He's been around for many years and I have a lot of respect for him."
There was also three-set wins for fellow seeds Nicolas Almagro and Kei Nishikori.
Almagro, the No 10 seed, overcame the 24th-ranked Jerzy Janowicz 7-6 (7-3) 7-6 (7-4) 6-1, while 16th seed Nishikori beat Evgeny Donskoy 7-6 (7-3) 6-2 6-3.
Janko Tipsarevic, the eighth seed, came through a five-set epic against No 32 seed Julien Benneteau with a 3-6 6-4 2-6 6-4 6-3 win.
There was an upset as well as 22nd seed Fernando Verdasco let a 2-1 lead slip as he lost 4-6 6-3 4-6 7-6 (7-4) 6-2 to Kevin Anderson.