Djokovic has not played since his shock second round exit at the Australian Open in January, and showed signs of ring-rustiness before defeating Klizan 6-3, 7-6 (7/4) before a raucous Mexican crowd.
The 29-year-old Serbian started slowly and was forced to save two break points in the third game of the first set before hanging on for a 2-1 lead. He had to save a further break point in the fifth game to take a 3-2 lead but then swiftly punished world number 62 Klizan with a break to go 4-2 up.
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The contest then went with serve as Djokovic claimed the opening set.
Klizan was soon in trouble in the second set as he suffered a break in the opening game before Djokovic held for 2-0.
That proved to be the cue for a mini-collapse, however, as Djokovic was broken twice and Klizan raced into a 4-2 lead.
But the 27-year-old Slovak's composure deserted him and Djokovic broke back and held to level at 4-4.
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The set went with serve to go into a tie-break and once again Djokovic's superior experience of pressure situations told, Klizan snatching at a forehand that went long to give his opponent match point.
Djokovic duly sealed the win with a deft lob that left Klizan scrambling to return before finishing with a volley into an open court.
Elsewhere on Tuesday, Australia's Bernard Tomic wilted in the sultry conditions against American Donald Young before retiring citing the heat.
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Tomic lost the first set in a tie-break 7-6 (7/5) but then retired before the second set got under way.
In other matches, third seed Maric Cilic advanced to the second round with a 6-3, 4-6, 6-0 win over Alexandr Dolgopolov of Ukraine.
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