"I am totally exhausted. I have no energy," the 20-year-old Djokovic told the crowd after the 6-7 7-6 5-7 7-5 7-6 triumph that lasted four hours 44 minutes on Louis Armstrong Stadium.
"I smelled my shoes, they are so stinky, but it's always good to win those matches."
Both players needed rubdowns to relieve the leg cramps that threatened to end the match at any moment. When Djokovic won the the final tiebreaker 7-2 he fell to the court in a mixture of fatigue and jubilation.
"It's tough to be proud when you lose, but I have a great feeling from that match," said world number 35 Stepanek. "I gave all I had. I know I had my chances, but that's life."
There were no major upsets at the National Tennis Center although former champions Marat Safin and Lleyton Hewitt were both sent packing.
Hewitt, the 2001 champion and 16th seed, was beaten by Argentine Agustin Calleri 4-6 6-4 6-4 6-2 while Russia's Safin, winner in 2000, was upended in three sets by Swiss Stanislas Wawrinka.
Number two seed Rafael Nadal showed no effects from a nagging knee injury, breezing by Janko Tipsarevic, 6-2 6-3 3-2 when the Serbian retired with a rib injury.
On the women's side, top seed Belgian Justine Henin needed just 50 minutes to crush 6-0 6-2 Russian qualifier Ekaterina Makarova, while number three Jelena Jankovic of Serbia weathered a 4-6 6-2 6-3 third-round challenge from 17-year-old
BIG MISTAKE
"I underestimated my opponent because I thought she was a junior that I would have an easy job," said Jankovic, an Open semi-finalist in 2006. "That was a big mistake for me.
"She gave me a really hard time, but I managed to somehow stay positive out there."
Twice champion and eighth seed Serena Williams also worked harder than expected, defeating Russian Vera Zvonareva 6-4 7-6 during two hours of spotty play on Arthur Ashe Stadium.
"I was upset after the match," said Williams. "I felt like I didn't play well at all. But that's said and done. I'm moving on."
Williams' sister, Venus, fared much better, beating Ukranian Alona Bondarenko, 6-1 6-2 in less than hour, boosted by a 30-5 advantage in winners.
Fifth seed Ana Ivanovic had little trouble with Russian Vera Dushevina, winning the third-round match 6-1 6-3 to set up a round of 16 affair with Venus Williams.
While many of the top seeds had to work harder than expected, the buzz around Flushing Meadows was about the Djokovic match. Huge crowds unable to enter the sold-out stadium watched the affair on large television screens.
Inside the stadium, the standing-room-only crowd cheered wildly on every point.
"We had an unbelievable fight, a remarkable match," said Djokovic, a 20-year-old Serb who will face Argentine Juan Martin Del Potro in the fourth round.
"We should both be proud. Of course, it's always good to be the winner of such a five setter."
