Fourth-seeded Roger Federer also got through, shaking off a slow start before dispatching Czech player Lukas Rosol 6-4, 6-1 in a little under one hour.
Having looked a little rusty in the second round on Wednesday, where he trailed 3-1 against Teymuraz Gabashvili, Nadal was more clinical this time and raced into a 4-0 lead.
"I think today I played a little bit better than yesterday," Nadal said. "For a long time I was playing at a good level, changing the directions very well, playing with the right intensity."
The top-seeded Nadal was only briefly troubled in the second set when Seppi broke him to love to pull back to 4-3 down. But Seppi could not hold and Nadal completed the victory with an ace on his first match point.
Nadal has a 21-5 career record against Ferrer, winning 10 of the past 11 meetings since Ferrer beat him in straight sets at the Australian Open in 2011 — the year he also lost to Nadal in the Monte Carlo final.
"David is a tough, tough player on any surface," Nadal said. "But here on clay, always a big challenge. I play a lot of matches against him, very tough ones."
Nadal won the tournament eight times in succession before losing last year's final to Novak Djokovic — who was in action later against Spaniard Pablo Carreno Busta.
Third-seeded Stanislas Wawrinka of Switzerland, and eighth-seeded Milos Raonic of Canada also advanced to the last eight.
Having taken only 46 minutes to win his second-round match, Wawrinka didn't even need to lift a racket after Spaniard Nicolas Almagro pulled out because of pain in his left foot.
"After consulting with the doctor for a long time this morning, we decided together that it was better for me not to play," the 15th-seeded Almagro said.
Wawrinka next faces the big-serving Raonic, who beat No. 11 Tommy Robredo of Spain 6-3, 6-4.
Tsonga won 5-7, 6-3, 6-0 against 10th-seeded Fabio Fognini of Italy, who did his best to spoil the Frenchman's 29th birthday with his wild antics, including smashing rackets and shouting loudly.
"Fabio is always like this. This is why we love him, he's a friend," Tsonga said. "But also I know that, if you let him, he's going to take 10 minutes before he plays the next point. I can't let him do that."
Nadal, however, thinks Fognini has to calm down or risk becoming a target for the boo boys.
"I know he's a good guy because I know him, but all the fans that are in the crowd saw him doing these things, probably they have a different opinion," Nadal said. "That's negative for him. So if he's able to understand that, he will change that."
- Sports & Recreation
- Rafael Nadal
- Andreas Seppi
- Roger Federer