The two-time runner-up Djokovic straight-setted Luxembourg left-hander Gilles Muller 6-1, 6-4, 6-4, but the Serbian star required a medical timeout on Day 5 to loosen up the left side of his body.
The eight-time Grand Slam champion Djokovic extended his current winning streak to 24 matches.
The reigning Australian Open and Wimbledon champ needs a French Open title to complete a career Grand Slam. He lost to Nadal in last year's final and in the 2012 championship match.
Up next for Djokovic will be promising young Aussie Thanasi Kokkinakis.
The third-seeded Murray improved to 12-0 on clay this year by holding off capable Portuguese Joao Sousa 6-2, 4-6, 6-4, 6-1.
The two-time Grand Slam champion Murray was this year's Aussie Open runner-up to Djokovic. The British star is a two-time French Open semifinalist, including last year.
His third-round opponent will be 29th-seeded Aussie slugger Nick Kyrgios, who received a walkover into the round of 32 on Wednesday.
The former world No. 1 Nadal, seeded sixth at this particular fortnight, blew away fellow Spaniard Nicolas Almagro 6-4, 6-3, 6-1 on Court Chatrier.
The 14-time Grand Slam champion Nadal has now won his last 37 matches at Roland Garros, where he's won the last five titles. He captured four straight French Open titles from 2005-08.
Nadal's trying to become the first man to win 10 titles at one major tournament.
Ninth-seeded U.S. Open champion Marin Cilic reached the third round by handling Italian Andrea Arnaboldi 7-6 (7-3), 6-1, 6-1. Cilic's next opponent will be in-form Argentine Leonardo Mayer.
Quality 17th-seeded Belgian David Goffin moved on by defeating Colombian Santiago Giraldo 6-3, 4-6, 7-5, 6-2.
In other second-round action involving seeds, Spaniard Pablo Andujar upended No. 22 German Philipp Kohlschreiber 6-1, 7-6 (7-5), 3-6, 3-6, 6-4, a No. 23 Mayer topped Poland's Jerzy Janowicz 6-4, 6-4, 6-7 (1-7), 6-1 and the aforementioned Kokkinakis tripped up No. 27 fellow countryman Bernard Tomic 3-6, 3-6, 6-3, 6-4, 8-6. Mayer was a clay-court runner-up in Nice last week.
Also on Thursday, Russian Andrey Kuznetsov bested Austrian veteran Jurgen Melzer 6-1, 5-7 (7-0), 7-6, 7-5.
And thanks to his next opponent's withdrawal, Japan's Kei Nishikori became the first player to reach the second week of the French Open.
The fifth-seeded U.S. Open runner-up was supposed to play Benjamin Becker in the third round on Friday, but the German Becker pulled out of the tournament Thursday because of a muscle tear in his right shoulder.
That puts Nishikori in the fourth round at Roland Garros for the second time. In 2013, he became the first man from Japan to make it that far in 75 years.
Next for Nishikori will be a fourth-round match on Sunday against Czech Lukas Rosol or Russian Teymuraz Gabashvili.