The UAE face Sri Lanka in the semifinals of the Global qualifiers on Sunday. The winner of this match will qualify for this year's Women's T20 World Cup
Djokovic won 6-3, 6-3 in testing, blustery conditions to set up a semi-final against Spain's Fernando Verdasco.
If the 38-year-old Stepanek had won he would have been the oldest player to have qualified for an ATP semi-final in almost 25 years, since a 40-year-old Jimmy Connors reached the last four in San Francisco in 1993.
"It's exciting, you obviously want to start the year off in the best possible way, that's three wins out of three," said Djokovic immediately afterwards.
"It's always a great test in these kind of consition, it's never easy for the players."
Djokovic, the defending champion in Doha, dominated throughout the 91-minute match.
He is on course to meet the man who took away his world number one spot at the end of last season, Andy Murray in Saturday's final.
Murray was due on court later on Thursday against Spain's Nicolas Almagro in another last-eight clash.
Earlier, Verdasco won through easily 6-2, 7-5, against another veteran, Ivo Karlovic.
The giant Croatian, 37, is currently ranked 20 in the world and is the oldest top 20 player since 43-year-old Ken Rosewall in 1978.
The semi-final line-up will be completed on Thursday when Tomas Berdych and Jo-Wilfried Tsonga, the number three and five seeds in Doha, face off.
And the night was not over for Stepanek, who rushed off court to play in the doubles' semi-finals with partner Vasek Pospisil.
The UAE face Sri Lanka in the semifinals of the Global qualifiers on Sunday. The winner of this match will qualify for this year's Women's T20 World Cup
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