No. 7 seed Kei Nishikori battled through a five-set clash against Frenchman Benoit Paire, winning 6-2, 6-7 (8), 6-2, 6-7 (8), 7-5 in just under four hours.
In the women's draw, America's Madison Keys downed Katerina Siniakova in straight sets and No. 8 seed Ashleigh Barty won 6-3, 3-6, 6-0 against Sofia Kenin.
Men's Fourth Round Results
(1) Novak Djokovic bt. Jan-Lennard Struff: 6-3, 6-2, 6-2
(7) Kei Nishikori bt. Benoit Paire: 6-2, 6-7 (8), 6-2, 6-7 (8), 7-5
Women's Fourth Round Results
(8) Ashleigh Barty bt. Sofia Kenin: 6-3, 3-6, 6-0
(14) Madison Keys bt. Katerina Siniakova: 6-2, 6-4
For a look at all Monday's results, visit RolandGarros.com.
Since winning the French Open for the first time back in 2016, Djokovic has been knocked out at the quarter-final stage in two successive visits to Roland Garros.
Given his form so far at the 2019 tournament, the world No. 1 will not be expecting a third last-eight exit in a row, although he will face a tough match against either Alexander Zverev or Fabio Fognini.
The Serb's clinical defeat of Struff on Monday was his fourth consecutive straight-sets victory this year in Paris. He has yet to even be taken to a tiebreak in the tournament.
Struff put up some resistance early on in the pair's fourth-round clash, valiantly saving a break point in the second game of the match by winning a baseline rally against Djokovic.
It always looked as though the 29-year-old was just clinging on, though, and at 4-3 ahead on serve Djokovic had another break opportunity, which he duly took with a smash.
The 15-time Grand Slam champion served out the opening set and then broke again for a 1-0 lead in the second:
From there it was effectively a procession.
Djokovic offered up just one break point in the whole match, which he saved, and he hit 31 winners to Struff's 20.
Perhaps most indicative of Djokovic's fine form is the fact he hit just 12 unforced errors in the 93 minutes he was out on court, seven of which came in the third set when the victory was all but sealed.
Nishikori had to put in much more effort to get past Paire.
Resuming play at the start of the fourth set on Monday after the match was suspended on Sunday, home favourite Paire forced a deciding set by winning his second tiebreak of the match
Having saved two match points late in the fourth, the world No. 38 then led 4-1 and 5-3 in the decider, but Nishikori produced consecutive breaks to maintain his remarkable record in five-set matches:
Unfortunately for the Japanese player, he now faces an in-form and fresh Rafael Nadal on Tuesday in the quarter-finals.
The women's draw looks wide open after some high-profile exits over the weekend, and Barty and Keys will both have designs on winning the tournament after making the quarter-finals, where they will face each other.
Keys, 24, reached the semi-finals at Roland Garros last year and was clinical in the French capital on Monday as she dispatched Katerina Siniakova in 76 minutes.
Barty, who had never before got past the second round at the French Open, looked under some pressure when Kenin forced a decider.
But the American slightly fell apart in the third, making numerous errors which Barty took full advantage of to book her spot in the last eight.