Djokovic, who reached the French Open semifinals last year, will face either Jean-Rene Lisnard or Albert Montanes.
"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."
Murray twice dropped serve to trail 2-1 in the opening set, but the Scot 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 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 the winner between Marin Cilic and Fabio Fognini. If Murray wins, he will reach a clay-court quarterfinal 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."
Hewitt won the U.S. Men's Clay Court Championships on Sunday for his first title in two years. He also won his first clay court tournament since Delray Beach in 1999.
But the 28-year-old Australian said he was exhausted after his flight was delayed out of Dallas, Texas.
"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 three and a half hours, as well, out of Dallas."
Hewitt had his right thigh massaged at the end of the first set and played with a wrap on it.
"It's a bit sore at the moment," Hewitt said.
"I don't remember ever playing so badly. Nothing was right. Nothing was working. My forehand, my backhand, my serve, nothing," Simon said.
In first-round matches, the 10th-seeded David Ferrer beat Feliciano Lopez 6-2, 6-3 in an all-Spanish meeting; 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.
Montanes, Lisnard and Martin Vassallo Arguello of Argentina also reached the second round.