The second-seeded Spaniard tormented his 43rd-ranked opponent with his mix of power and accuracy to seal victory in less than two hours on Court Suzanne Lenglen.
Nadal, bidding to surpass the mark of six Roland Garros titles he jointly holds with Swede Bjorn Borg, prevailed on his first match point with his 19th forehand winner.
Nadal, who has only dropped nine games in his first two matches and lost only one match since his debut on the Paris clay in 2005, will next face Argentine
Although he reckoned his first serve still needs some adjustments, Nadal was happy on all accounts.
"I improved during the third set. This is when I had the upper hand. I played my best tennis. I made almost no mistakes," Nadal said.
"It was a dream type of third set. In general, I feel really good."
Nadal also feels happier as a person.
"I said I felt better, but I was not saying my season's going to be better. I was saying that during practice and during the tournament my attitude is slightly more positive, and it's less difficult," he explained.
"Whereas last year, due to my attitude, which was less positive, it was more difficult for me. The rallies were longer, and I was not at home and I felt it was a bit long.
"This year I'm having fun, a lot of fun, I'm happy, and I'm not - how can I say? I'm not suffering from the fact that I'm far from home."
Nadal, however, hopes he will celebrate his 26th birthday in Paris for the seventh time in eight years, having always won the title after blowing out his candles at Roland Garros.
"It is difficult to celebrate a good birthday when you are in the middle of the tournament, but sure, I'm gonna go for dinner with the team,” he added.
"I don't know if some of my family are going to come. I don't know yet. The important thing is I am in the third round and hopefully I can celebrate the birthday in Paris and not in Mallorca."
The fifth-seeded Tsonga was level at one set all and 1-1 in the third when play resumed after being interrupted by rain on Wednesday and he was just too sharp for the world number 90.
Tsonga, the last Frenchman to reach a Grand Slam final, at the 2008 Australian Open, started with a break and never looked back on Court Philippe Chatrier.
He spent just under an hour on court to finish off Stebe and set up a meeting with Italian
Spanish sixth seed
He will face 27th seed
Murray next plays
In the second-longest match in French Open history, home player
The Argentine goes up against 19th seed
He will face German