Djokovic starts Paris defence with win, Rublev and Hurkacz both through in straight sets
Djokovic, a six-times winner at the ATP Masters 1000 event in the French capital, was made to toil in the opening set by Cressy but emerged unscathed after the American double-faulted twice in the tie break.
The Serbian raised his game in the second set, breaking his opponent at 4-4 before serving out the match with ease.
"It was very intense, just a lot of pressure. When you play someone that serves this well - first and second serve - you don't have much room to relax and maybe play kind of a softer few games," said 21-time major champion Djokovic.
"A break came at the right time, perfect time actually. I was very pleased with the way I held my serve, didn't face a break point."
Earlier, Rublev was solid on return as he broke the big-serving John Isner (37) three times to progress 6-2 6-3 in just over an hour and claim his first win in four career meetings against the American.
"It is a really important win at this moment when I am fighting for Turin," said Rublev who is vying for one of the two remaining spots at the season-ending ATP Finals.
"I think I was a bit lucky. It was his first tournament since his bad injury. From the baseline I was feeling really confident. As soon as I was returning and the ball was in play, I felt I had an advantage and wasn't nervous."
Poland's Hurkacz fired 20 aces and saved eight break points to overcome French left-hander Adrian Mannarino (34) 7-6(5) 6-4 to stay on a course for a potential third-round clash against Rublev.
Third-seeded Casper Ruud (23), who has already qualified for the ATP Finals, defeated French wildcard Richard Gasquet (36) 6-1 7-6(7) after a thrilling second set, where the Norwegian bounced back from 3-5 down.
In the other matches, French qualifier Corentin Moutet (23) downed Borna Coric (245) 3-6 6-3 6-4 and Dan Evans (32) of Britain saw off American youngster Brandon Nakashima (21) 6-3 3-6 6-4.
