French hopes of a first home win in 33 years, meanwhile, were dealt a heavy blow when sixth-seed Jo-Wilfried Tsonga retired with a groin injury in the first set of his match with Ernests Gulbis.
Djokovic, who can become just the eighth man to win all four Grand Slam tournaments should be emerge triumphant next weekend, beat Britain's Aljaz Bedene 6-2, 6-3, 6-3 just before the light became too poor to play in.
"It was important to finish this evening," was Djokovic's relieved comment on his late show before thanking the umpire for keeping the action going despite the gloom.
Williams, seeking an Open-era, record-equalling 22nd Grand Slam title, was a set up and about to tackle a second set tie-break against France's Kristina Mladenovic when a thunderstorm sent everyone scurrying for cover.
On the resumption, more than two and a half hours later, the top seed and defending champion needed five match points to finish the job going through 6-4, 7-6 (12/10) with Ukraine 18th seed Elina Svitolina next in her line of fire following her victory over former champion Ana Ivanovic.
"I feel like I made a tremendous amount of errors. But, you know, I feel like she kind of forced me to. She forced me to go for it, and unfortunately, I wasn't hitting great today."
Thiem was already done and dusted ahead of the rain, downing German teenager Alexander Zverev 6-7 (4/7), 6-3, 6-3, 6-3 to reach the fourth round.
In what was a clash of two of the sport's rising new stars, the Austrian dropped a tight first set, but then coasted away from his 19-year-old opponent.
22-year-old Thiem has reached the quarter-finals of a Grand Slam and Tsonga's exit will further improve his chances.
"It's been the third match in the last four weeks between us and it was really tough, but I knew that from the start already," he said.
"It was my first match on one of the big stadiums (at Roland Garros) and it was packed. An unbelievable experience."
Also through to the last 16 was 2014 losing finalist David Ferrer, who comfortably saw off the challenge of fellow Spaniard Feliciano Lopez 6-4, 7-6 (8/6), 6-1.
Belgian 12th seed David Goffin beat Nicolas Almagro 6-2, 4-6, 6-3, 4-6, 6-2 and next plays Gulbis.
In the women's tournament, there were wins also for eighth seed Timea Bacsinszky of Switzerland, Spain's Carla Suarez Navarro and Kazakhstan's Yulia Putintseva, who reached the last 16 of a Grand Slam tournament for the first time.
- Venus excited -
=================
Venus then made it a daily double for the Williams sisters with a 7-6 (7/3), 1-6, 6-0 win over Alize Cornet of France.
That put the 35-year-old into the fourth round in Paris for the first time since 2010 and heading for a possible semi-final showdown with her sister.
Late in the day Madison Keys made it four Americans in the last 16 with a 7-6 (7/3), 6-3 over Monica Puig of Puerto Rico.
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