Murray and Federer advance at Indian Wells
Andy Murray pictured during a Mexico ATP Open in Acapulco on February 28, 2014 - by Pedro Pardo
Murray, the Wimbledon Champion who has yet to reach a final since undergoing back surgery in September, asserted himself in the second and third sets for a 4-6, 6-3, 6-2 victory over the 49th-ranked Czech.
World number one Rafael Nadal was waiting in the wings to launch his title defence with a second-round night match against Czech Radek Stepanek.
In the meantime, a bevy of big names moved into the third round.
Four-time champion Roger Federer got past France's Paul-Henri Mathieu 6-2, 7-6 (7/5).
Former world number one Federer has fallen to eighth in the world and is seeded seventh here.
But despite the decline in his ranking, the Swiss great arrived in the California desert fresh from claiming a 78th career ATP title in Dubai last week, his first title in nine months sparking anticipation he could add to the Indian Wells titles he won from 2004-2006 and in 2012.
Fellow Swiss Stanislas Wawrinka -- seeded third in his first tournament since his surprise Australian Open triumph -- downed Croatian Ivo Karlovic 6-3, 7-5.
Women's top seed Li Na, who won her second Grand Slam title at the Australian Open in January, won an all-Chinese clash with Zheng Jie 6-1, 7-5, and Slovakian Dominika Cibulkova, runner-up to Li in Melbourne, advanced with a 6-3, 6-2 win over Croatian Donna Vekic.
For Murray, it was a bit of a battle in the early going, something he's familiar with at Indian Wells.
Murray reached the final on the hardcourts of the California desert in 2009, but he had lost his openers in two of the past three years.
"Here I have always kind of struggled at the beginning of the tournament," Murray said. "I don't know if it's the conditions or whatever reason it is, but I have never really started this tournament that well.
"I think it's important sometimes to think about it, because when you're not expecting it to happen and then it does, that's when it can take you by surprise and you might panic a little bit or worry.
"Today, I was a set and a break down. I got broken three times in a row at the end of the first set, beginning of the second. You know, I just kind of kept going and found a way to win, which is always the most important thing."
Rosol used his booming forehand to good effect in the opening set, but was eventually undone by 51 unforced errors.
"When the ball is sitting there, he hits it extremely well," Murray said. "He hits it hard. He puts pressure on you.
"In the second and third sets, I was dictating a lot more of the points. I would use my forehand a lot more. I was a lot more active on my feet in between shots to look for the right shots."
Murray, seeded fifth, next faces exciting young Czech Jiri Vesely, a 6-1, 2-6, 6-1 winner over Spain's Pablo Andujar.
Elsewhere in Murray's quarter of the draw, Colombia's Allejandro Falla came back from 2-5 down in the third set to beat 18th-seeded Jerzy Janowicz of Poland 6-3, 2-6, 7-6 (7/5), saving one match point on the way.