The 34-year-old Stepanek, ranked 34th in the world, did little wrong in an entertaining clash of inspired shotmaking and ball-chasing, but the Serb's court craft, service return and retrieval skills were simply too good in the end.
"Always great to play Radek. He's very experienced, very tricky to play. Hope you enjoyed as much as we did on the court," said 25-year-old Serbian after he reached the fourth round for the seventh year in a row.
While Djokovic never really looked like he might lose the match, he had few opportunities to truly dominate and had some luck as well with several net cords going in his favour.
An exasperated Stepanek managed to get some respite from the net in a 14-minute first game of the third set when his shot clattered into the cord and dropped over into Djokovic's side of the court.
Djokovic's forehand lunge went into the net and he then proceeded to vent mock frustration at the net and the Czech, who simply thrust out his chest with arms outstretched and looked to the sky as the crowd burst into applause and laughter.
Stepanek saved six break points in that first game and the match went on serve until Djokovic did enough to snatch the break in the 11th to give him the opportunity to serve out.
Not that Stepanek allowed him a cake walk into the fourth round as he saved one match point by scrambling up, down, back, left and right to slam an over-the-shoulder forehand at Djokovic that set up a winning passing shot.
"He loves the big stage; you saw how much fun he had. I also had a lot of fun playing," Djokovic said. "It was a very entertaining match."
Mindful of his 1-7 career record against the Serbian, the 34-year-old Stepanek refused to sit on the baseline and trade shots with Djokovic, approaching the net 67 times to try to cut down the angles and force his opponent to take risks.
"He is a very talented player, very skilful. He made a lot of great first volleys and made me play the extra ball," Djokovic said.
"He was chipping and charging; not a lot of players do this any more, a lot of the players stay on the baseline.
"He never gives you the same ball twice. That's something that makes him a different player from most of the guys."
The top seep is seeking to become the first man to win three successive Australian Open titles since the tennis went professional in 1969.
Djokovic will now meet big-serving Switzerland's Stanislas Wawrinka in the fourth round, with Wawrinka having beaten American Sam Querrey 6-6 7-5 6-4.
The absence of the injured world number four Rafa Nadal has left a gaping hole in the top half of the draw and fourth seed David Ferrer eased further into it with a 6-4 6-2 6-3 win over another entertainer, 2006 finalist Marcos Baghdatis.
The Spanish baseliner showed more than a few decent touches of his own - most notably a sumptuous backhand lob - as he set up a fourth-round contest against Japan's Kei Nishikori.
Big-serving Tomas Berdych was a 6-3 6-2 6-2 winner over Jurgen Melzer and will face Kevin Anderson in the next round with a likely quarter-final meeting with Djokovic on the line.
"Kevin Anderson has a huge serve so it could be like playing against myself," the Czech fifth seed said of the South African, who upset 22nd seed Fernando Verdasco 4-6 6-3 4-6 7-6 6-2.
Janko Tipsarevic had a much tougher time as he came through a five-set epic against Julien Bennetau, eventually winning 3-6 6-4 2-6 6-4 6-3 in cool, windy conditions.
"The weather in Australia, I have to say it's crazy," the world number nine said after his 3-6 6-4 2-6 6-4 6-3 victory over France's Julien Benneteau.
"You don't know what are you going to get.
"I mean, three days ago it was really cold when I played Lacko. Two days ago it was like 70 degrees Celsius on the court.
"Today was beautiful, but it was really, really windy.
"Who knows what's going to happen tomorrow? Probably we'll have rain and we're going to end up playing indoors.
"You really need to adjust on a day to day basis to this grand slam."
Tipsarevic, who has never made it beyond the third round at Melbourne Park before, now faces Nicolas Almagro in the last 16 and he hoped he did not have to contend with another heat blast against the Spaniard having played successive five-set matches.
"I am pretty fit at the moment, but these matches are actually not helping me," he said in reference to his three hour, 29 minute clash against Benneteau and the three hours, 51 minutes he spent on court against Lukas Lacko in round two.
"If I'm really wanting to go deep into the tournament, potentially playing Nicolas Almagro on the heat, my legs are going to feel the five set matches which I played in the last two rounds.
The Serbian will next face Spanish 10th seed Nicolas Almagro, who ended Jerzy Janowicz's maiden Australian Open with a 7-6 7-6 6-1 win in a match that was free of the histrionics that accompanied the Pole's second round victory.