With a third title in his sights, the Spaniard recorded a 4-6 6-3 6-3 6-3 victory, and will now face his 2012 nemesis Lukas Rosol in the second round.
Rosol, who beat Benoit Paire in his opener, sent Nadal crashing out at the same stage two years ago and will hope to repeat that feat on Thursday.
The world number one had a shaky start on Tuesday as Klizan caused him problems and created three break-point chances in the opening game of the match.
He survived those, but he was not so lucky eight games later as Klizan moved 5-4 ahead before serving out for a shock first-set lead.
Nadal's service games were by no means solid in the second set but he was able to make the crucial break at 3-2 up.
That appeared to give the second seed confidence and he upped his performance in the third set to win the opening three games.
Nadal maintained his concentration and, after a 42-minute set, was ahead for the first time in the match.
Victory was assured in just under three hours as Nadal again pressured the Klizan serve and, although he was broken himself, he sealed his progression by converting his second match point.