Djokovic was rarely troubled in beating Oscar Hernandez of Spain 6-1, 6-2, while Murray began slowly before defeating Victor Hanescu of Romania 6-3, 6-2 to stay on course for a first career quarterfinal match on clay.
Djokovic, who reached the French Open semifinals last year, next faces either Jean-Rene Lisnard or Albert Montanes. The Serb said he was surprised at how well he played in his first clay-court match of the season.
"I didn't quite expect to perform that good, considering the fact that I didn't have any matches, singles matches, on this surface,'' Djokovic said. "But I was really playing aggressive and patient at the same time. This combination is really important for this surface. So hopefully I can continue.''
Murray twice dropped serve early to trail 2-1 in the opening set, but the British player took the next four games for a commanding lead.
"At the start of the match when I got broken, I was sort of moving like I was still on a hard court,'' Murray said. "And then after four, five, six games, I started to move better.''
He broke Hanescu, a French Open quarterfinalist in 2005, in the seventh game of the second set to take a 5-2 lead, and then converted his fourth match point when the Romanian hit a forehand return into the net.
Murray, who lost to Roger Federer in the U.S. Open final last year, next takes on either 14th-seeded Marin Cilic or Fabio Fognini of Italy. If he wins that, he will reach a clay-court quarterfinal match for the first time in his career.
"It takes time. I never played that well on clay especially in the last couple of years,'' Murray said. "I played solid and he made some mistakes. I was happy with the way I played for my first match on clay this year.''
Also in the second round, sixth-seeded Gilles Simon lost to Andreas Beck of Germany 7-5, 6-1. Simon, who twice beat Federer last year, said the loss to a qualifier was the worst he could recall.
"I don't remember ever playing so badly. Nothing was right. Nothing was working. My forehand, my backhand, my serve, nothing,'' Simon said. "I played so bad today that I couldn't have beaten anyone.''
Marat Safin of Russia beat Lleyton Hewitt 6-4, 7-5 in a match between two-time Grand Slam champions. Safin next plays Nicolas Lapentti of Ecuador.
Hewitt won the U.S. Men's Clay Court Championships on Sunday for his first clay-court tournament since 1999. But the 28-year-old Australian player felt exhausted after his flight out of Dallas, Texas, was delayed.
"I couldn't get out Sunday night,'' Hewitt said. "And then Monday, with the time change and everything, it just sort of put it even further behind. Then our flights got delayed about 3 1/2 hours, as well, out of Dallas.''
Hewitt had massage treatment on his right thigh at the end of the first set and continued the match with a bandage.
"It's a bit sore at the moment,'' Hewitt said.
In the first round, 10th-seeded David Ferrer beat Feliciano Lopez 6-2, 6-3 in an all-Spanish match; No. 12 David Nalbandian of Argentina beat Paul-Henri Mathieu of France 6-4, 3-6, 6-3; and Janko Tipsarevic of Serbia upset ninth-seeded Gael Monfils of France 6-3, 6-1.
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