Tsonga had not won a Masters 1000 match since Madrid in 2017, but fought back from a set down to beat Rublev 4-6 7-5 6-4.
Cilic eased past Hubert Hurkacz of Poland 7-6(5) 6-4 to set up a second round meeting with three-time Grand Slam champion Stan Wawrinka.
Roland-Garros
'You don't see it with Rafa, Novak and Roger' - Wilander on younger tennis stars
26/05/2022 AT 10:40
The 2014 U.S. Open champion dictated the contest with power and precision as he won 86% of his first-serve points to seal his third consecutive victory over Hurkacz in less than two years.
Big-serving Canadian Raonic capitalised on fast court conditions to outclass Britain's Cameron Norrie 6-3 6-2 in just over an hour at the AccorHotels Arena.
A back injury has limited Raonic to three matches since the Rogers Cup in August, but the 2014 Paris runner-up was back to full strength as he struck 14 aces in a masterful display.
Raonic will next face newly-crowned Vienna Open champion Dominic Thiem.
Earlier in the day, world number three Roger Federer pulled out of the tournament as he fine tunes his schedule heading into the season-ending ATP Finals.
Federer, Novak Djokovic, Rafa Nadal, Daniil Medvedev, Thiem and Stefanos Tsitsipas have booked their places for next month's ATP Finals, with the Paris Masters set to determine who clinches the final two spots for the London tournament.
Italian Andreas Seppi has replaced Federer as a lucky loser in the Paris main draw and will meet Moldova's Radu Albot in the second round.
Roland-Garros
'Without Federer tennis is almost a different sport' - Zverev
25/05/2022 AT 09:14
Roland-Garros
'Those guys are very selfish!' - McEnroe on why Tsonga failed to win a Grand Slam
24/05/2022 AT 21:06