Djokovic, trying to become the first man in the Open era to win all four majors on at least two occasions, won the contest on Court Philippe Chatrier after two and a half hours. Djokovic, however, recovered in time to put away his nerves, and his opponent for a passage into the next round.
The Serbian tennis star wins their meeting in straight sets, taking the match 6-3, 6-4, 6-2.
But the Dane, making her 10th appearance at Roland Garros, showed her greater experience at key moments, winning both her breaks points in the opening set while the Australian converted just one out of five.
Ferrer, seeded 30, took his first-round record at Roland Garros to 15-0 with a 5-7 6-3 4-6 6-3 13-11 victory.
Provided the seedings work out he will meet Lucas Pouille in the fourth round, Dominic Thiem in the quarter-finals and Rafael Nadal in the semi-finals.
And so he did, with the second set getting right back on serve.
Rafael Nadal (pic) will face big-serving Dutchman Robin Haase in the French Open today.
Svitolina converted all three break points and hit 25 winners to prevail 6-4, 6-3 over Yaroslava Shvedova, a two-time quarterfinalist in Paris.
Despite the defeat, Fourlis walked off to a standing ovation.
Also seeing early wins are fifth seeded Milos Raonic and third seeded Stan Wawrinka.
The Canadian will next play either Rogerio Dutra Silva of Brazil or Russian Mikhail Youzhny.
Muguruza's victory was an emphatic one and the manner in which she overcame a former champion was impressive however her performance certainly was not flawless.
- The match was halted on Monday due to poor light and rain and play resumed on Tuesday with the scores tied at a set apiece.
Meanwhile, reigning women's champion Garbine Muguruza put aside her middling for this season to begin her Roland Garros defence with a 6-2, 6-4 victory over 2010 victor Francesca Schiavone. "Not remembering how I played a year ago".
Spanish veteran Feliciano Lopez has defeated Bjorn Fratangelo 6-4 7-6 (7-4) 6-3, while Croatian 20-year-old Borna Coric saw off Mathias Bourgue 7-6 (7-5) 6-3 6-2.
Since beating Andy Murray in last year's final, Djokovic has failed to add any more major titles to his collection. Djokovic's last Grand Slam title was at the French Open a year ago.