The Spaniard, looking for his eighth Roland Garros title, looked ill at ease as fellow left hander Klizan came out swinging and dropped the first set before raising his game enough to claim victory in two hours 44 minutes.
In the third round, number two seed Roger Federer eased past France's Julien Benneteau 6-3 6-4 7-5 to reach the fourth round in awe-inspiring fashion.
There was the usual array of running aerial forehands, gravity-defying drop shots and whipped backhands as the former world number one booked a meeting with French 15th seed Gilles Simon who beat American Sam Querrey 2-6 6-3 2-6 7-6 (2) 6-2.
Benneteau, the 30th seed, broke in the first game to open a 2-0 lead but 17-times Grand Slam champion Federer kept his cool and turned the situation around in no time.
Benneteau, who has been struggling with a groin problem, bowed out on the first match point when he could not retrieve another powerful Federer forehand.
Federer left Court Philippe Chatrier on a standing ovation from the Paris crowd.
"You are so nice to me," Federer said courtside with a smile. "I'm sorry for Julien, he looked diminished," he added after a 91-minute tennis masterclass.
Benneteau started with an exquisite crosscourt forehand winner and took the first game on Federer's serve but the Frenchman, who beat the Swiss in Rotterdam this year, could not sustain the pace.
At 3-3, Federer upped the tempo, winning 14 points in a row to snatch the opening set and he started the second in convincing style with some jaw-dropping shots.
The second game of the second set lasted just 45 seconds and Federer flicked a sublime backhand into Benneteau's feet to break decisively in the ninth game.
Benneteau continued to fight in the third, but Federer, who won the title in Paris in 2009, was simply too good.
He has now dropped 23 games over three straight-set victories.
"I'm happy because I have not used much of my energy so far," said Federer.
"I feel totally relaxed. Mentally I'm okay. I'm quite confident. I can feel it, which is what you need to be if you want to go deep and have good results here at Roland Garros."
Thursday's heavy rain meant Nadal's match was one of several second-round ties held over and having not played since Monday, and the Spaniard was clearly not firing on all cylinders against Klizan.
On Monday he was pushed hard by Daniel Brands and world number 35 Klizan had obviously taken a leaf out of the German's book with some heavy hitting from the baseline to break the misfiring Spaniard's serve in the eighth game.
Klizan brought up set point with a second serve ace and claimed the opener in 40 minutes.
Nadal surged 4-0 ahead in the second but 23-year-old Klizan remained a threat and recovered one of the breaks of serve.
Third seed Nadal took the second set and then moved a break ahead in the third but wobbled at 3-2 when Klizan earned two break points, only to squander his chance to draw level.
Klizan's challenge then faded and Nadal, without looking totally convincing and carelessly dropping serve late in the fourth set, secured a Saturday clash with Italian Fabio Fognini.
Jo-Wilfried Tsonga continued his march towards a potential quarter-final with Federer by reaching the fourth round with a 6-1 6-2 7-5 win over fellow Frenchman Jeremy Chardy.
Sixth seed Tsonga, the highest-ranked French player in the singles draws, next meets Serbian Viktor Troicki.
"I was more solid than in the previous round," said Tsonga.
Asked how he would spend his day off, he replied: "I'm not going shopping because I'm not allowed to ... I'm not allowed to cuddle either because it's energy-sapping. There's not much I'm allowed to do so I'm going to practise."
Tsonga, who has yet to drop a set, took 102 minutes to dispose of Australian Open quarter-finalist Chardy on Court Philippe Chatrier.
The 28-year-old Tsonga, as usual, relied on a big serve and a booming forehand and ended 25th seed Chardy's ordeal on his second match point with a service winner.
Tsonga said he loved playing on courts made heavy by damp weather.
"I feel good when it's heavy because it gives me time to strike the ball and also gives me time to run from one ball to the next because it's going slower," he said.
"I can have my power from the baseline felt by the opponent."
But there was double despair for France after wildcard Gael Monfils's 2-6 6-7 (5) 6-2 7-6 (3) 6-2 defeat by Tommy Robredo of Spain and Benneteau's loss to Federer.
Monfils, who has recently been hampered by a nagging knee injury, wasted four match points before crumbling in the decider.
Earlier, home hope Richard Gasquet advanced to the third round. The seventh seed demolished Poland's Michal Przysniezny 6-3 6-3 6-0 and next plays Russian Nikolay Davydenko.
American marathon man John Isner soothed the memory of his record-breaking loss at last year's French Open with victory over Ryan Harrison in another five-set epic.
A year to the day that he lost to local favourite Paul-Henri Mathieu in a 76-game battle, the most ever played in a men's match at Roland Garros, Isner held off young gun Harrison to win 5-7 6-7 (7) 6-3 6-1 8-6 in three hours 50 minutes.
The 19th seed looked to be on the way out after dropping the opening two sets in a second-round match held over from Thursday but struck back to grind down his 21-year-old rival.
After sealing victory, the 28-year-old was bent double after another brutal encounter and clearly relieved after ending a six-match losing sequence in matches going to five sets.
Isner, who faces Tommy Haas next, holds the overall all time record for the longest professional match in history when he beat France's Nicolas Mahut 6-4 3-6 6-7 7-6 70-68 at Wimbledon in 2010. The match lasted 11 hours and five minutes.
David Ferrer - the fourth seed - beat fellow Spaniard Feliciano Lopez 6-1 7-5 6-4 in the first match of the third round and will next face Kevin Anderson, who became the first South African to reach the fourth round of the French Open since 1996 when he out-slugged 14th seed Milos Raonic.
The 27-year-old, Africa's only men's singles main draw entrant, won 7-5 7-6(4) 6-3 in a match he dominated with his serve to equal the feat of Wayne Ferreira.
In doing so, the six-foot-eight-inch Anderson also equalled his best ever Grand Slam showing having also reached the last 16 at the Australian Open earlier this year.
"Wayne is a great player to aspire to and to try and reach some of his achievements," Anderson said.
"He was a great player and I've still obviously got a long way to go to...but being in the fourth round is great. A lot of people think clay is not a good surface but I enjoy playing on it."
Ferrer will be a different type of contest to the one against the giant Raonic and Anderson is hoping for warmer, drier weather in time for Sunday's fourth round.
"I think it might help," said the South African after delivering 16 aces. "The serve might bounce up a little bit more and it may be easier to control points and get the ball up a little bit.
"I think that would be a bit more to my advantage."
2-Roger Federer (Switzerland) beat 30-Julien Benneteau (France) 6-3 6-4 7-5
4-David Ferrer (Spain) beat Feliciano Lopez (Spain) 6-1 7-5 6-4
6-Jo-Wilfried Tsonga (France) beat 25-Jeremy Chardy (France) 6-1 6-2 7-5
Viktor Troicki (Serbia) beat 10-Marin Cilic (Croatia) 7-6(12) 6-4 7-5
11-Nicolas Almagro (Spain) beat 20-Andreas Seppi (Italy) 7-6(1) 6-0 6-4
23-Kevin Anderson (South Africa) beat 14-Milos Raonic (Canada) 7-5 7-6(4) 6-3
15-Gilles Simon (France) beat 18-Sam Querrey (U.S.) 2-6 6-3 2-6 7-6(2) 6-2
32-Tommy Robredo (Spain) beat Gael Monfils (France) 2-6 6-7(5) 6-2 7-6(3) 6-2
3-Rafa Nadal (Spain) beat Martin Klizan (Slovakia) 4-6 6-3 6-3 6-3
7-Richard Gasquet (France) beat Michal Przysiezny (Poland) 6-3 6-3 6-0
8-Janko Tipsarevic (Serbia) beat Fernando Verdasco (Spain) 7-6(3) 6-1 3-6 5-7 8-6
9-Stanislas Wawrinka (Switzerland) beat Horacio Zeballos (Argentina) 6-2 7-6(2) 6-4
12-Tommy Haas (Germany) beat Jack Sock (U.S.) 7-6(3) 6-2 7-5
19-John Isner (U.S.) beat Ryan Harrison (U.S.) 5-7 6-7(7) 6-3 6-1 8-6
21-Jerzy Janowicz (Poland) beat Robin Haase (Netherlands) 6-4 4-6 6-4 6-3
29-Mikhail Youzhny (Russia) beat Federico Delbonis (Argentina) 6-3 6-7(5) 7-5 6-4
Nikolay Davydenko (Russia) beat Denis Istomin (Uzbekistan) 6-4 7-5 6-2