The Spaniard, in his first match as defending champion, was stretched to the limit before prevailing 2-6 6-4 7-5 in night match that lasted two hours, 24 minutes in the California desert.
Nadal served eight double faults and was broken three times, but he also broke his Czech opponent three times, including twice in the final set.
The pivotal moment came in the sixth game of the third set, when Nadal fended off three break points to hold serve.
Fifth seed Murray recovered from a slow start to beat his Czech opponent 4-6 6-3 6-2 as the top seeds took to the courts for the first time after receiving first round byes.
"I got broken three times in a row the end of the first set, beginning of the second," Murray told reporters. "I just kind of kept going and found a way to win, which is always the most important thing."
Only five active players have won more tour-level hardcourt matches, headed by Roger Federer (575).
Seventh seed Federer dominated the first set but was taken to a tie-break in the second before prevailing 6-2 7-6(5) against French qualifier Paul-Henri Mathieu, while Swiss compatriot and Australian Open champion Stanislas Wawrinka clinched a 6-3 7-5 win over Croatia's Ivo Karlovic.
Australian Lleyton Hewitt failed to notch his 600th career win when he was beaten by South African Kevin Anderson 7-6(5) 6-4.
The veteran Hewitt saved 10 of 11 break points but was unable to break the tall 17th seed's powerful serve in the match.
There was high drama in another match as Colombian Alejandro Falla saved a match point at 5-2 down in the third set to beat Polish 18th seed Jerzy Janowicz 6-3 2-6 7-6(5).
On the women's side, top seed Li Na beat Chinese compatriot Zheng Jie 6-1 7-5.
Australian Open champion Li notched six breaks as Zheng struggled on serve.
Defending champion Maria Sharapova made short work of her first match, beating German Julia Goerges 6-1 6-4 in barely an hour.
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- Andy Murray
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