"I'm happy about these four matches". In the victory, Djokovic won 72 percent of his first serve points and 47 percent of his second serve points.
The French 13th seed is through to just her second Slam quarterfinal - after the 2015 US Open - and will face Switzerland's Timea Bacsinszky for a spot in the last four.
Britain suffered its third major attack in three months when men using a van and knives killed seven people in a busy area of London on Saturday night.
It's Djokovic's eighth straight trip to the quarterfinals at Roland Garros as he seeks to repeat as champion.
He will now face Pablo Carreno Busta, who beat Milos Raonic, in the quarter-finals where victory will be his 100th in best-of-five-set matches on his beloved clay.
Fifth seed Svitolina downed Pole Magda Linette 6-4, 7-5.
Djokovic was soon back in control, though, and wrapped up victory with a cross-court forehand victor.
Muguruza, who was seeded No. 4 in Paris, beat Serena Williams in the French Open final previous year. Mladenovic took the opener 6-1.
Time will tell if Thiem has learned anything from those defeats, but this match has the potential to run to five sets. One of the earlier ones ended at 9-7, the other at 8-6.
Muguruza was asked after the match about the cries of "forza" - Italian for "come on" - which Mladenovic had uttered after some of her opponent's errors.
Teenager Jelena Ostapenko is the first woman from Latvia to make it to the French Open quarterfinals in the professional era.
In the men's doubles India's Purav Raja and Divij Sharan showed stomach for a fight but eventually went down 4-6, 7-6 (5), 2-6 to American Ryan Harrison and New Zealand's Michael Venus.
Seeded winners in the women's third round: No. 3 Simona Halep, No. 11 Caroline Wozniacki, No. 21 Carla Suarez Navarro, No. 28 Caroline Garcia.
French 15th seed Gael Monfils reached the fourth round for a seventh time when compatriot Richard Gasquet withdrew from their rain-delayed match with a thigh injury.
Nadal, seeking a record 10th championship at the clay-court major, overwhelmed Roberto Bautista Agut 6-1, 6-2, 6-2 and has dropped only 20 games so far.
"Nadal is at his best", the 17th-seeded Bautista Agut said. He won in less than two hours. "It's very important for me to be in the quarter-finals one more time", said Nadal, who turned 31 on Saturday.
He will face another Spaniard, Pablo Carreno Busta, in the last eight.
Big-serving American John Isner, who was seed number 21, was knocked out in his third-round match by Karen Khachanov of Russian Federation, who won 7-6 (7-1) 6-3 6-7 (5-7) 7-6 (7-3).
Isner was the last USA man in the draw of 11 who entered the tournament.