Djokovic, the top seed who is looking for a fifth Miami Masters crown, had to work for his 6-0, 5-7, 6-1 second-round victory over Klizan.
The world number one, who beat Roger Federer last weekend for the Indian Wells crown in California, is hoping to duplicate his North American March hardcourt title double of last year.
In fact, the Serb is bidding to become the first man to complete the sweep three times.
He looked well on his way to a quick win when he snapped up the opening set against his 41st-ranked opponent in 23 minutes.
He won the first seven games before Klizan got onto the scoreboard and appeared set to serve out a quick victory with a 5-3 lead in the second.
But he dropped his serve and Klizan went on to win the second set before Djokovic re-established control and earned the victory after one hour, 56 minutes.
"Credit to Klizan for battling and making me play an extra shot," said Djokovic. "It was a pretty different game in the second set than it was in the first. But in the third I managed to bounce back and get a win."
Djokovic next plays Belgian qualifier Steve Darcis, a 6-4, 6-7 (2/7), 6-3 winner over Gilles Muller.
"I hope to have another great week in Miami," said Djokovic of his quest for another career milestone. "I've played some of my best tennis on these courts."
In other men's matches, Japanese fourth seed Kei Nishikori defeated Russian Mikhail Youzhny 6-2, 6-1.
Canadian fifth seed Milos Raonic beat Teimuraz Gabashvili 6-1, 6-4 while Spanish sixth seed David Ferrer beat Argentine Federico Delbonis 6-1, 6-1.
In the women's third-round play, fourth-seeded Dane Caroline Wozniacki, Russian eighth-seed Ekaterina Makarova and ninth-seeded German Andrea Petkovic all advanced.
Venus Williams also booked a fourth-round berth, with a 6-4, 7-6 (7/3) victory over Australian Samantha Stosur.
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