World number two Djokovic had to work hard to take the opening set, but after he saved three break points early in the second it was plain sailing for the 26-year-old in front of a 17,000-strong home crowd.
Having come out on top in several long rallies in the opening stages, Stepanek faded as his more resourceful opponent began tormenting him with stinging baseline shots at the Kombank Arena.
Retrieving like a terrier everything Stepanek threw at him, Djokovic broke the Czech in the ninth game of the third set and then held serve to seal the match and draw a standing ovation from the fans.
Serbia's Dusan Lajovic, a late replacement for the injured Janko Tipsarevic, takes on world number seven Tomas Berdych in the day's other singles rubber.


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