The Serb's new supercoach has left Paris for other previous engagements but there was no visible withdrawal symptoms for Djokovic, who battled early and cruised late to notch a 7-6 (5), 6-1, 6-3 victory over Spaniard southpaw Albert Ramos-Vinolas.
Thiem has never beaten Djokovic in five previous meetings, with the Serbian also beating the No.6 seed in the French Open past year, when Thiem had no answer in a straight set loss in the semifinals.
"I'm sure he's going to be as motivated as ever, so I expect him to come out and really play his best".
Rafael Nadal produced another dominant display to race into his 11th French Open quarter-final.
Nadal now has a 76-2 win-loss record at Roland Garros with his only defeats coming against Robin Soderling in the fourth round in 2009 and Djokovic in the 2015 quarter-finals. He beat Grigor Dimitrov to reach the fourth round at the French Open and score his first win over a player in the top 13 of the ATP Tour rankings. "I respect him a lot".
Ostapenko defeated Samata Stosur of Australia 2-6, 6-2, 6-4.
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Earlier, women's defending champion, Garbine Muguruza, and seven-time Grand Slam victor Venus Williams crash out of the French Open, meaning a new major singles champion will be crowned at Roland Garros.
Two weeks past his 21st birthday, unseeded Karen Khachanov of Russian Federation became the youngest man to reach the French Open's fourth round since 2009, beating 21st-seeded American John Isner 7-6 (1), 6-3, 6-7 (5), 7-6 (3).
Before thinking about the prospect of facing Nadal in the last four, Djokovic's first task is to overcome sixth seed Dominic Thiem.
No. 15 Gael Monfils of France was leading 7-6 (5), 5-7, 4-3 against Richard Gasquet in the 3rd round when his countryman retired after getting treatment on his right thigh.
Four women's singles third round encounters still need to be played, including Czech second seed Karolina Pliskova against Germany's Carina Witthoeft and Ukrainian fifth seed Elina Svitolina versus Poland's Magda Linette.
However, Garbine Muguruza crashed out in the last 16.
This was the second year in a row that Bacsinszky beat seven-time major champion Venus Williams in the fourth round in Paris.
"Svetlana's a great player, especially on clay so I knew it wouldn't be easy", said Wozniacki, a two-time US Open runner-up.