The Serb, unlike in his slick second-round win, looked rusty in only his second singles match since playing in the Davis Cup six weeks ago, losing a 4-1 lead in the first set and squandering three break opportunities early in the second.
The 24-times Grand Slam winner mounted a comeback, however, as he convincingly won the tiebreak and took the decider to continue his quest for a record-extending seventh title in Paris.
"I run out of steam, I've been struggling the last couple of days with my stomach, I didn't feel myself at all on court," Djokovic said.
"It could've run easily on his way, but I played a good tiebreak and started to feel better on the third. I'm really happy I overcame this challenge."
Fourth seed Jannik Sinner withdrew from the tournament, citing health reasons after his second-round clash against Mackenzie McDonald ended at 2:37 a.m. on Thursday.
The Italian was due to play Australia's Alex de Minaur, who will now face in-form Andrey Rublev, the fifth-seed Russian who earned his 20th Masters 1000 win of the season by beating qualifier Botic Van de Zandschulp 6-3, 6-3.
Seventh seed Stefanos Tsitsipas secured his spot at the ATP Finals with a 7-6(2), 6-4 win over German 10th seed Alexander Zverev. The Greek will play Karen Khachanov in the quarter-finals after the 16th seed beat fellow Russian Roman Safiullin 4-6, 6-4, 6-2.
Poland's Hubert Hurkacz, the 11th seed, remained in contention for a spot at the tournament in Turin by beating Argentine Francisco Cerundolo 6-4, 6-3.
He will meet Grigor Dimitrov for a place in the semi-finals after the Bulgarian routed Alexander Bublik 6-2, 6-2.
In the last act of the evening, defending champion and sixth seed Holger Rune claimed a comfortable 6-3 6-3 win over Daniel Altmaier. The Dane will face Djokovic in a rematch of last year's final.
