Seventh seed Ferrer, who has again been one of the most impressive performers on clay this season and could prove a real threat to the likes of Rafael Nadal and Novak Djokovic, took only an hour and 25 minutes to see off Jarkko Nieminen 6-3 6-3 6-1.
Home favourite Tsonga followed the Spaniard on to Court Philippe Chatrier and, although his 6-3 6-2 6-2 scoreline against Jan Hajek was just as emphatic, that did not tell the whole story.
Both players struggled with the wind, which whipped up the dry clay, and 17th seed Tsonga needed to save break points at the end of the first set before making his extra power count.
The Frenchman said: "I dominated him throughout. It was not obvious because of the gusts of wind. It was not my best type of tennis but, given the conditions, it was not bad."
Stanislas Wawrinka, who could meet Swiss compatriot Roger Federer in the last 16, certainly did not have the ideal first set against French qualifier Augustin Gensse but fought back to win 4-6 6-3 6-4 6-2.
The 14th seed said: I'm satisfied. I expected, like every year, the first match not to be too easy.
"He played really well. I took some time before I got into the match. But I felt better at the end and I'm glad I won in four sets."
Cilic reached the fourth round at Roland Garros in 2009 and 2010 but he lasted less than three hours at this year's tournament before losing 7-6 (7-5) 6-4 6-4. The Croatian, seeded 19th, staged a fightback from 1-5 down in the third set but Spanish clay-court specialist Ramirez Hidalgo kept his nerve to pull off an impressive upset.
Yesterday's defeat was the latest of a frustrating season for Cilic, 22, who looked set to become a fixture in the top 10 when he reached the Australian Open semi-finals last year but he will now fall further from his current ranking of 20th.
It was also a miserable day for Latvia's Ernests Gulbis, once considered one of the sport's next big stars but who yesterday suffered his sixth successive first-round defeat at grand slams, losing 6-1 6-4 6-2 to Blaz Kavcic.
Two of the lower seeds in the men's draw progressed, with Guillermo Garcia Lopez (30) beating Robert Kendrick 6-1 7-5 4-6 6-3 while 31st seed Sergiy Stakhovsky recovered from a set down to defeat French qualifier David Guez 6-7 (7/9) 6-3 6-3 6-3.
There was some disappointing news for the organisers before the start of play, meanwhile, when former world No 1 Lleyton Hewitt withdrew after failing to recover from injury. The Australian's place went to French veteran Marc Gicquel but he could not make the most of his second chance and lost 6-4 6-4 6-2 to Albert Montanes.
Hewitt has been increasingly troubled by injuries in recent years, chiefly hip problems, but an injury to his left ankle was given as the reason for his absence in Paris this week.
World No 64 Hewitt, who reached top spot in the ATP rankings in 2001, has never made it past the quarter-finals in the claycourt grand slam.
Andy Roddick, Juan Carlos Ferrero and Tommy Robredo have all pulled out of the tournament in recent days while Serena and Venus Williams announced they would not be heading to France earlier this week.
After yesterday's low-key start, today's men's schedule is packed with stars, including Federer and the in-form Novak Djokovic, who will look to make it a remarkable 40 matches unbeaten when he takes on Dutchman Thiemo De Bakker.