Nadal, a losing finalist to Roger Federer last year in Melbourne, will face Bosnia-Herzegovina's 28th seed Damir Dzumhur in the third round.
Leonardo Mayer saved five of the eight break points he faced and converted five of his seven chances to beat David Ferrer in the clay court tournament.
Andy Murray connected on only 57 percent of his first serves but was broken only once in the match, yet that was primarily because of his ability to chase down balls from the South American shotmaker.
Kei Nishikori equalled his best performance at Wimbledon as the Japanese 12th seed reached the third round with a 7-6 (7/5), 6-4, 6-2 victory over Argentina's Leonardo Mayer on Thursday.
Mahesh Bhupathi-Julian Knowle beat Argentine-Spanish duo Leonardo Mayer and Albert Ramos 6-2, 6-7(5), 6-4, 6-2 in two hours and 37 minutes in the first round clash.
Mayer's sudden withdrawal left Nadal feeling a little flat, but the Spaniard was quite animated when describing the earthquake, which originated from an epicentre just 30 miles (50 km) from Indian Wells.