Fifth seed Murray recovered from a slow start to beat his Czech opponent 4-6 6-3 6-2 as the top seeds finally took to the courts in the Californian desert after receiving first round byes.
Briton Murray won 69 per cent of his second serves, compared to just 39 per cent by Rosol, which proved a key difference.
"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).
- Sports & Recreation