The world number one had taken a 31-0 record into the contest as he had not lost a match at Roland Garros since his debut at the claycourt grand slam in 2005.
But Soderling paid little attention to the script as he brought the world number one down on his knees to cause one of the biggest shocks ever seen in Paris.
"I told myself this is just another match," said the jubilant Soderling.
"All the time, I was trying to play as if it was a training session. When I was 4-1 up in the tiebreak, I started to believe."
Six-times grand slam champion Nadal looked weary on Centre Court, losing the first set in 34 minutes before rallying back to win the second in a tiebreak 7-2.
It was not enough to break Soderling's resilience as the 23rd-seeded Swede broke once in the third to take the lead and snatched the fourth set tiebreak 7-2, wrapping up the win after three hours 30 minutes on his second match point.
Half-hearted
A half-hearted Ana Ivanovic surrendered her crown without much of a fight when she was totally outclassed in the fourth round by a Belarussian teenager who never lost belief.
Victoria Azarenka has been rising up the ranks steadily and she finally announced her arrival on the big stage when she condemned the Serbian eighth seed to a 6-2, 6-3 defeat.
As Ivanovic bid an early farewell to Roland Garros, 19-year-old Azarenka set up a quarterfinal date with champion-in-waiting Dinara Safina.
The Serb, who has been struggling with a right knee injury and played with black tape over the area, has suffered a dip in form since winning at Roland Garros last year and has slipped from number one to eighth in the world.
The ninth-seeded Azarenka, who has won three titles this year, took command after breaking in the third game and clinched the first set when Ivanovic's forehand clipped the netcord and bounced back into her side of the court.
The 19-year-old Belarussian surged to a 5-2 lead in the second before Ivanovic, her crown hanging by a thread, fought back with a couple of excellent passing shots and a dropshot to break.
It is the first time she has reached the last eight at a grand slam.
The Russian top seed's headlong charge towards a maiden grand slam title showed no sign of running out of steam as she flattened Aravane Rezai 6-1, 6-0.
Third seed Andy Murray made the most of Marin Cilic's errors to reach his first French Open quarterfinal, clobbering the Croat 7-5, 7-6, 6-1.
After a tentative start where they traded breaks, the Briton seized the initiative in the 11th game and served out the set when Cilic could not control his return after a searing delivery.
Cilic, who made 40 unforced errors to Murray's 14, got himself into trouble with some poorly controlled forehands and eventually surrendered the second set tiebreak with one that flew wide.
The 20-year-old Croat called the trainer on for treatment on a thigh problem before Murray raced to a 4-0 lead in the third. Serving for the match, the Scot unleashed a powerful shot that was met with yet another wild forehand from Cilic. The win not only made him the first Briton to reach the last eight since 2004 but kept Murray in the race against Roger Federer to secure the world number two spot by the end of the tournament.
Stamping her mark
Former world number one Justine Henin urged Safina to stamp her mark on the sport and the Russian appears to have taken the message to heart, dropping only five games in four rounds at the claycourt major.
"I don't waste my energy. I want to win every point," said the 23-year-old, who has bagged four of the eight sets she has contested to love.
"I'm just surprised that it's really like five games that I lost before getting into the quarters. It's not a bad feeling, and I hope if I continue like this I can go a long way."
Slovak Dominika Cibulkova made it through to the last eight of a grand slam for the first time when she outwitted Hungarian Agnes Szavay 6-2, 6-4.
The 20th seed sealed victory over Venus Williams's conqueror with a sweetly struck forehand down the line after a long rally.
Fernando Gonzalez lived up to his nickname of 'Speedy' as he darted into the last eight with a 6-2, 6-4, 6-2 win over Romanian 30th seed Victor Hanescu.
The Chilean, who will next face Murray, has yet to drop a set at this year's event.
