Nadal took the first step towards a third clay title this season by defeating Ukrainian qualifier Oleksandr Dolgopolov 6-4, 6-3.
Murray, seeded third and desperate to start turning a so-so season on clay, beat Juan Ignacio Chela for the fourth time in a row, earning a 6-3, 6-3 opening victory after a bye in the first round.
"I was pleased with the win," said Murray. "I served well and was able to move him around the court.
"It will be the same tomorrow (when he plays Romanian Victor Hanescu). He's a tall guy and the serves will be booming. I have to take control to win."
Nadal and Murray both won the event when it was played indoors on hardcourt during the autumn, with Nadal taking the title in 2005 and Murray following up in 2008.
The Spaniard, second seed behind Roger Federer, didn't need to produce much second-round spectacle for his eager home fans as he methodically dispatched number 62 Dolgopolov with three breaks of serve and little else required.
Nadal, who has titles this season from Masters 1000 outings at Monte Carlo and Rome, won his 11th match in a row on clay this season in just under 90 minutes.
"It was difficult to play against him, he's very fast, said Nadal, calling the win "an important victory for me".
"I'm happy with it, but sometimes I did not have the match under control. I must do better tomorrow."
Nadal will have to lift his game on Thursday when he takes on 2.05-metre American John Isner, a comeback winner over Santiago Giraldo of Colombia 1-6, 7-6 (8/6), 6-2.
The 13th-seeded Isner made a breakthrough at the weekend as he lost in a rare all-American European clay final in Belgrade.
"Isner is one of the most dangerous players on tour," said Nadal.
"The pressure is very big on your serve. If you lose it against him you are unlikely to be able to come back in the set."
Marin Cilic, the Croatian eighth seed, beat Argentine Edoardo Schwank 6-3, 6-0. Latvian Ernests Gulbis, a semi-finalist in Rome, upset Russian number 10 Mikhail Youzhny 7-6 (7/2), 6-4.
French 12th seed Gael Monfils needed only 11 minutes to go through as German Philipp Petzschner quit at 1-1 with a leg injury after informing his friend in advance that he was in pain.
But Monfils's compatriot Jo-Wilfried Tsonga withdrew as a precaution with back pain after losing a first set 6-2 to Guillermo Garcia-Lopez.
"This is something I've had before. It usually takes about a week to heal. I first felt it last Friday practising, so I thought it would be smarter to withdraw as a precaution since Roland Garros is now so close," said Tsonga.
Stanislas Wawrinka set up a third-round meeting with Federer after Argentine Leonardo Mayer quit with an arm problem at 6-4, 4-2 in their match.
Off-court, Andy Roddick was forced out before his second-round start after unsuccessfully trying to overcome a stomach virus.
The pullout from the fifth seed and world number eight came before his opening match against Madrid's Feliciano Lopez, who later defeated Oscar Hernandez of Spain 6-1, 6-2.
In women's WTA play, Jelena Jankovic said she took little notice of compatriot Ana Ivanovic across the net, emerging with a scratchy 4-6, 6-4, 6-1 win in a Serbian struggle for the third round.
"I treated it as just another match," said the seventh seed, a beaten finalist in Rome last weekend.
"Maybe at the start of our careers it was important. Now you just want to play your tennis."
Spain's Arantxa Parra Santonja claimed the last of the third-round places, defeating China's Peng Shuai 1-6, 7-6 (7-1), 6-3.
In the third round, Venus Williams beat Italian Francesca Schiavone 3-6, 6-1, 6-2 but top seed Serena crashed out to Nadia Petrova 4-6, 6-2, 6-3.