Djokovic has not played since his shock second round exit at the Australian Open in January.
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.
"I wasn't expecting an easy match, that's for sure," said Djokovic. "The field here is very strong and I got a collision in the first round against a guy who is well known for playing his best tennis on the big stage."
"But all in all it was a good performance to win in straight sets. A tough second set but it's exactly what I needed at this moment to test myself and my game and I'm looking forward to the next challenge."
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.
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.
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 Tuesday, another former world number one Rafael Nadal eased into the second round with a straight sets victory over Germany's Mischa Zverev.
Nadal took 1hr 17min to advance past the world number 30 6-4, 6-3.
Australia's Bernard Tomic wilted in the sultry conditions against American Donald Young before retiring citing the heat.
Tomic lost the first set in a tie-break 7-6 (7/5) but then retired before the second set got under way.
Tomic's fellow Australian Nick Kyrgios survived a scare in his opening round game before defeating Israel's Dudi Sela in three sets, winning 3-6, 6-3, 6-3.
In other matches, third seed Marin Cilic advanced to the second round with a 6-3, 4-6, 6-0 win over Alexandr Dolgopolov of Ukraine.