World number one Nadal was tested by Spanish compatriot Roberto Carballes Baena, but - playing on the court named in his honour - he ultimately recorded a comfortable 6-4 6-4 win.
Second seed Grigor Dimitrov of Bulgaria also moved smoothly past Frenchman Gilles Simon 6-2 6-1 to reach the last 16.
Djokovic was drawn in the same half as Nadal in both the Monte Carlo Masters and the Barcelona Open, but the Serb, who is just making his way back to full fitness after a long injury absence failed to get past the opening three rounds in both the tournaments.
26 de abril de 2018, 14:04Barcelona, Spain, Apr 26 (Prensa Latina) Rafael Nadal says he had to change his mentality to beat Guillermo Garcia-Lopez in the Barcelona Open or Conde Godo this afternoon.
Serving for the match, Klizan double-faulted but he had three chances to close out and clinched the second when another Djokovic forehand missed its mark.
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The Slovak impressively dismantled Novak Djokovic on Tuesday to book his spot in the third round and he now awaits Rafael Nadal, should the world No. 1 come through his tie later.
"Definitely, I expect higher from myself", Djokovic said.
Only Guillermo Coria (35) and Ilie Nastase (34) have ever topped 30 straight sets.
Nadal, a dominant player at both Monte-Carlo and the Barcelona Open, was the favorite there and remains the favorite this week.
Nishikori, who lost to Nadal in the Monte Carlo Masters final on Sunday, was trailing 6-3 before retiring with pain in his right thigh.
Djokovic's start to the year, which now stands at five wins and five losses, is the worst of his entire professional career.