Both Gonzalez and Soderling, who won 6-1, 6-3, 6-1 against Russian 10th seed Nikolay Davydenko, will be contesting their first Roland Garros semi-final, while Soderling had never before advanced beyond the third round at a major.
Gonzalez, the 12th seed, tasted Grand Slam heartache when he lost to Roger Federer in the final of the 2007 Australian Open.
But he looked in excellent form against Murray, who broke into the world top three after a superb start to 2009 that saw him win three tournaments.
"His forehand is the biggest in tennis," Murray said of Gonzalez, who won 6-3, 3-6, 6-0, 6-4.
"If you look at some of the shots he´s hit, he´s hitting forehands from like a metre wide of the tramline on some points and hitting winners off them.
"Even if you try to hit a ball to his backhand, he makes his mind up that he wants to hit a forehand and he runs around it and spanks a winner. You can´t do a whole lot with it."
Gonzalez admitted that he had tried to dominate with his forehand and said it was a shot that came to him naturally.
"I´ve been hitting the same for years and years. I always try to attack, I have no fear and I just go for it.
"I know if I have to win important matches I´ll do it on that side."
Gonzalez, 28, took the first set after a crashing forehand down the line but Murray, the third seed, appeared to have figured out how to counter his hard-hitting opponent when he won the second set to level the match.
The third set, though, was a disaster for the Scot, who was guilty of a string of loose shots as Gonzalez conspired to break him three times in succession.
Murray, a losing finalist at last year´s US Open in his first Grand Slam final, sought to rouse himself in the early stages of the fourth set and looked set to mount a stirring comeback when Gonzalez allowed himself to be broken while serving for the match at 5-3 up.
It proved a temporary reprieve, though, as Murray handed Gonzalez three match points with a netted drop shot before seeing a forehand clip the top of the net and bounce back on his side to confirm his exit from the competition.
Soderling, the 23rd seed, followed up his defeat of four-time champion Rafael Nadal on Sunday with a surprisingly routine straight sets victory over Davydenko.
"I didn´t have a very easy draw," said the 24-year-old Soderling, who also overcame Spanish 14th seed David Ferrer in the third round.
"I´ve played three good claycourt players and I´ve played three very good matches, so my confidence is getting better and better."
Davydenko, playing on his 28th birthday, had no answer to Soderling´s strafing groundstrokes and pinpoint returning, with the Swede wrapping up the match in 1hr 41min.
"He played faster. I felt like he was always hitting balls right on the line," said Davydenko, the world number 11.
"I have no chance. I try to run, but I´m not Nadal."
After tamely conceding the first set, Davydenko stepped up his game at the start of the second but Soderling waited for his opportunity before breaking in game seven when the Russian found the net with a forehand.
Soderling continued to find the corners of the court in a very one-sided third set as he took another step towards becoming the first Swedish champion at Roland Garros since Mats Wilander in 1988.
Earlier in the day, pint-sized Dominika Cibulkova became the first Slovakian to reach the French Open semi-finals on Tuesday after striking down Russian giant Maria Sharapova 6-0, 6-2.
Now the 5ft 3in (1.61m) Cibulkova must tackle another mighty figure in the shape of world number one and top seed Dinara Safina, who reached her second successive semi-final here with a 1-6, 6-4, 6-2 win over Victoria Azarenka.
Sharapova, a three-time Grand Slam title winner, but who has never got beyond the last four in Paris, was playing just her second tournament following a 10-month lay-off to recover from a shoulder injury.
She had needed three sets in each of her four matches to make the last eight and the 22-year-old ran out of steam against an inspired Cibulkova, who is enjoying her best Grand Slam run.
Tuesday´s loss was former world number one Sharapova´s heaviest defeat since she went down 6-1, 6-1 to Serena Williams in the fourth round in Miami in 2007.
It could have been a lot worse as Cibulkova, the 20th seed, had a match point to complete a 6-0, 6-0 humiliation before the Russian managed to put two games together to stop the rot.
Had she suffered a whitewash, it would have been only her second ´double-bagel´ after she lost to Lindsay Davenport in the Indian Wells semi-finals in 2005.
Sharapova saved three more match points in the eighth game of the second set before her resistance crumbled.
"It took me a while to get going and create good opportunities to come to the net and finish the points," said Sharapova.
"But you can only ask your body to do so much. Everything fell short and the pace wasn´t there. It all combined but she played really solid and I came up short."
Cibulkova said she wasn´t surprised by her performance.
"It might be a surprising result for people who don´t know me but I played solid from the baseline and didn´t make too many errors," said the Bratislava girl.
"I knew that if I could make her move around the court I would have a chance."
Sharapova, whose world ranking slumped to 126 during her time off the tour, had won both her previous clashes against Cibulkova and both were on clay.
But Cibulkova, 11 inches (27cm) shorter than the glamorous Russian, was in complete control from the outset and claimed victory on a fifth match point when Sharapova put a weary return into the net.
Sharapova finished with 27 unforced errors to her opponent´s nine.
Fellow Russian Safina, still seeking a first Grand Slam title to back up her number one status, made the most of watching Belarusian ninth seed Azarenka´s game and hair-trigger temperament fall apart.
"She played well in the first set. I wasn´t doing anything. I played in her zone and hit down the middle and did all the running," admitted Safina.
"But then I fought hard and she missed too much."
Safina, the runner-up in 2008, had stormed into the quarter-finals having lost just five games in four rounds, but it took only 20 minutes on Tuesday for the 23-year-old to drop five more.
Azarenka had defeated Safina for the first and only time in four previous meetings on her way to the Miami title in March and the 19-year-old, who knocked out defending champion Ana Ivanovic in the fourth round, came out firing, spearing a succession of flat, deep, forehand and backhand winners.
Three breaks of serve gave the leggy blonde the opening set after just 21 minutes.
But Safina was in control of the rest of the tie and wrapped up her 19th win in her last 20 claycourt ties.
The remaining two quarter-finals take place on Wednesday with unseeded Romanian teenager Sorana Cirstea facing Australian 30th seed Samantha Stosur and Russian seventh seed up against world number two Serena Williams, the 2002 champion.
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