Djokovic, who is aiming to follow up last week's win at Indian Wells with his fifth triumph at Key Biscayne, took care of the first set in just 22 minutes but was broken when serving for the match at 5-3 in the second.
Klizan went on to turn the set around in his favour and had the packed crowd sensing an upset, but Djokovic regrouped and romped home in the third set.
Djokovic will face Belgian qualifier Steve Darcis in the next round.
Japan's Kei Nishikori made a confident start to his Miami Open bid beating Russian Mikhail Youzhny 6-2 6-1 in their second round meeting.
Nishikori, the fourth seed at Key Biscayne, won 70 percent of his service points and converted five of his 16 break chances.
"I felt really good on the court. Really confident," he said. "I was almost dictating the court against Misha, and serving well. Everything was good."
Jo-Wilfried Tsonga enjoyed victory in his first match back from injury with a 6-4 3-6 6-3 win over American Tim Smyczek.
The Frenchman had not played this year after picking up the injury in the Davis Cup final defeat to Switzerland in November.
“I didn't expect to play my best tennis today, but I'm happy the way I managed my match,” said Tsonga.
"I just had a little hole in the second set. But it's normal when I haven’t played in a couple of months now. I hope it's going to be better and better, but for the first match it was already something good for me."
Sixth seed David Ferrer of Spain beat Argentina's Federico Delbonis 6-1 6-1.
In an all-South American clash Brazil's Thomaz Bellucci beat Uruguayan Pablo Cuevas 2-6 6-2 7-5 and advanced to face Ukraine's Alexandr Dolgopolov, who beat 16th seed Tommy Robredo 6-7(1) 6-3 7-5.
(Editing by Gene Cherry/Peter Rutherford)
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