Nadal beat Finland's Jarkko Nieminen 6-4 6-3 while Djokovic defeated Italian Andreas Seppi 6-1 6-4.
Last year's finalist David Ferrer, the fifth seed, suffered a shock 6-3 6-2 loss to Brazilian Thomaz Bellucci.
Spaniard Nadal, who is chasing a record eighth consecutive victory in Monte Carlo, resumed full training last week after a right knee injury forced him to pull out of his semi-final clash with Andy Murray in Miami.
He showed no signs of the problem as he recorded his 40th win at the chic venue by the glittering Mediterranean, where he has been unbeaten since 2005.
Nadal wowed the crowd as he hit some dramatic forehand passes when Nieminen, 48th in the world, came to the net.
The second seed will next play Kazakhstan qualifier Mikhail Kukushkin, who defeated Italian Filippo Volandri 7-6 2-6 6-2.
Serbia's Djokovic, who is chasing Nadal's French Open crown after winning the last three grand slam events, had a flying start to go 4-0 up but was less impressive afterwards and needed 88 minutes to edge out Seppi - ranked 44th in the world.
Djokovic easily grabbed the first set but was made to work a little harder in the second as Seppi, who had lost their six previous ties, played more aggressively.
"For the first official match (on clay) since Roland Garros last year, it's satisfying," Djokovic told a news conference.
"We had a couple of long games but I served very well when I needed to."
The top seed will take on 16th seed Alexandr Dolgopolov, who beat Australian teenager Bernard Tomic 6-2 5-7 6-1, in the third round.
Djokovic, who beat the inventive Ukrainian in straight sets at last year's U.S. Open, said the threat would be bigger this time as clay favoured Dolgopolov's game.
"You expect the unexpected from him," Djokovic said.
"He comes up with some drop shots, he changes the pace very much. That's why he's very dangerous on clay, which is a slower surface and gives him more time to come up with his shots."
The unexpected happened on the central court as Bellucci destroyed world number six David Ferrer, who had a 24-3 ATP Tour record this season and won three titles including the Acapulco and Buenos Aires claycourt events.
The left-handed Brazilian, who was hammered in straight sets by Ferrer in their three previous ties, produced a fine combination of powerful forehands and defensive two-handed backhands to upset the Spaniard.
Czech Tomas Berdych moved past Croatia's Marin Cilic 7-6 6-1 while eighth seeded Spaniard Nicolas Almagro defeated Italian Potito Starace by the same score and next meets Swiss Stanislas Wawrinka.
Serb Janko Tipsarevic, the seventh seed, advanced after beating Spaniard Albert Montanes 6-2 6-3 in one hour 33 minutes and will next face Frenchman Gilles Simon, who hammered last year's quarter-finalist Federico Gil 6-3 6-0.
France's Julien Benneteau recovered from a break down in each set to upset 15th seed and last year's semi-finalist Juergen Melzer 6-4 6-3 to set up a third-round tie with Andy Murray.
