Meanwhile, Nadal had extended his tally of winning successive sets on clay-court to world record 38 Wednesday when he outclassed compatriot Roberto Carballes Baena 6-4, 6-4.
Klizan followed up his second-round win over Novak Djokovic by beating Spain's Feliciano Lopez 6-1 6-4.
The Serb has had a string of achievements on the clay surface in the past, culminating in winning the elusive French Open grand slam in 2016. But a reunion with long-time coach Marian Vajda this month had sparked hopes Djokovic could yet steer his career back on track.
My real motivation is just play, Monte-Carlo last week and now play Barcelona.
Known for his power and rock-solid defence, Nadal showed a deft touch to earn the opening break of the match and a 3-1 lead in the first as a backhand slice died dramatically on his opponent and only the net was found in response. He was then broken while trailing 4-3, allowing the qualifier to serve out for the victory.
His compatriot Guillermo Garcia-Lopez will face him on Barcelona's main court aptly named "Pista Rafael Nadal" in honour of the great clay-court champion, later on Wednesday with the victor taking on the inspired Klizan. "I haven't had too many matches in the last 12 months, so it's a lack of match play and a lack of these kinds of situations".
The 31-year-old will now face another Spaniard in Guillermo Garcia Lopez, who progressed after Kei Nishikori retired. "I haven't lived up to your expectations", he told a news conference. He is now being coached by former Tennis player Carlos Moya having been trained by his uncle Toni Nadal for almost 27 years. Thiem will next face Greek Stefanos Tsitsipas, who beat 10th-seeded Spaniard Albert Ramos-Vinolas 6-4, 7-5.