The top seed had to wait until the night match on Tuesday, the third day of the tournament in Paris, to begin his quest for a record-extending 25th Grand Slam title, but got going quickly, dispatching French wildcard Herbert 6-4 7 – 6(3) 6-4 on Court Philippe Chatrier.
The 37-year-old Djokovic has not reached a final this year and his world number one ranking is under threat from Australian Open winner Jannik Sinner.
But everything looked fine against Herbert, who put up solid resistance but never seemed to unduly worry the Serbian, who has now won 72 of his 74 first-round matches in Grand Slam tournaments.
The only problem came in the second set when the Serbian broke serve early, but then dropped his own serve and was dragged into a tiebreak before finding an extra gear to move towards victory.
“He caused me a lot of problems with his serving, serving and volleying, but for my part I am satisfied with the performance,” Djokovic told Eurosport. “At this age I see every match as a golden opportunity, because you don't know how long you have left at this level.”
Previously, Casper Ruud and Aryna Sabalenka shone on a cold, rainy day. They entered the second round with dominant victories, but the spectators at Roland Garros were largely out of action.
With the weather preventing any chance of play on the outdoor courts before 4pm (local time), the action was limited to the two main competition courts – Philippe Chatrier and Suzanne Lenglen – both with retractable roofs.
Twice runner-up Ruud defeated Brazilian qualifier Felipe Alves 6-3 6-4 6-3 in a renewed bid for a maiden Grand Slam title in Paris after disappointments in the previous two years.
Brimming with confidence after his triumph in Geneva, the world number seven produced a masterclass in serving as he raced past his unknown opponent in less than two hours.
“This is one of the biggest tournaments every year for me and for everyone. One of my highlights. I always look forward to it. The past two years have given me so much here,” said Ruud. “I hope I can make it another good year.”
Sabalenka was as fast as last year's semi-finalist, who is eyeing a second major of the season after her successful Australian Open defense, to mow down Russian teenager Erika Andreeva 6-1 6-2 in 68 minutes.
“I'm super happy to be back on this special field. Great to see you all supporting us today. It was a great atmosphere,” said Sabalenka. “I know you guys had no choice, it's raining outside so you had to be on this field, but anyway, thank you very much.”
Fourth seed Elena Rybakina overcame an early wobble to float past Belgium's Greet Minnen 6-2 6-3 earlier in the day, showing no signs of the illness that had hampered her preparations for the second major of the year.
The tournament's third consecutive rainy day started with a huge outpouring of love for Frenchwoman Alize Cornet, as one of the ever-present players at Grand Slams in the past two decades bowed out after her opening loss to seventh seed Zheng Qinwen.
Cornet, who holds the Open era women's record for consecutive Grand Slam main draws with 69, had previously said she would retire after the tournament.
Australian Alex De Minaur defeated Alex Michelsen, Petra Martic defeated Kristina Mladenovic and Arantxa Rus stunned three-time Grand Slam champion Angelique Kerber in the few matches played on the outdoor courts.