The defending champion will face David Goffin on Saturday after the Belgian beat Spaniard Roberto Bautista 6-7(3) 6-2 6-2.
Greek teenager Stefanos Tsitsipas also reached the last four after overwhelming third seed Dominic Thiem 6-3 6-2 and the 19-year-old will next face Spain's Pablo Carreno Busta, who served up another upset by defeating second seed Grigor Dimitrov 6-3 7-6(4).
World number 140 Klizan, who had knocked out Novak Djokovic in the second round, came within a point of being the first player since Thiem in May 2017 to win a set against the Mallorcan on the slow surface but the world number one's famed battling skills denied him that moment of glory.
After romping through the opening set, Nadal lost his focus and surrendered his serve at the start of the second set. But just as Klizan appeared to be on the verge of delivering a psychological blow, the 10-times Barcelona champion saved the set point at 4-5 down before breaking back to level.
He held in the next game to take the lead for the first time in the second set and then broke a tired Klizan to clinch his place in the semis.
"He played very aggressively and caused me a lot of discomfort... he was unpredictable and that caused me confusion. It was tough, but the important thing was not to fail," Nadal told a news conference.
Tsitsipas converted four out of eight break points and made Thiem pay for an error-strewn display to secure the biggest win of his career.
Thiem began the contest strongly and came within a point of going up 3-0 in the opening set but allowed Tsitsipas to fight back. The Greek won a decisive break to go ahead at 5-3 after a double fault by Thiem and then served out the set.
Tsitsipas broke at 2-2 in the second set after more wayward hitting by Thiem and the world number 63 pulled away to seal the match.
Carreno Busta, seeded fifth in Barcelona, saw off Dimitrov to reach his second semi-final of the year and level his head-to-head with the Bulgarian at three wins apiece.
