Defending champion Rafael Nadal produced his customary brand of high-impact tennis to overpower Tommy Haas 6-4 6-3 and secure his berth in the last eight where he will meet Czech number one Tomas Berdych, who toppled sixth seed Andy Roddick.
Nadal, the only remaining Spaniard in the tournament, responded to the vociferous support of a capacity crowd at the Madrid Arena with an aggressive display against his German opponent, giving the 13th seed little chance.
Federer, who is bidding to win his 10th title of the year, was pushed all the way by the 22-year-old Soderling and needed two tiebreaks and two challenges using the "hawk-eye" replay equipment to shake off his dogged opponent.
Neither player showed any sign of weakness on their serve and both sets went to tie breaks in a fiercely contested match.
Federer was 4-2 down in the second decider and had to save three set points and challenge Soderling's final two shots using the replay equipment as he clinched a 10-8 victory.
CRAZY END
"It turned out to be a crazy end and was kind of funny waiting for the result on the match point," said Federer. "But it wouldn't have made a difference to the end result."
He will meet Robby Ginepri in the quarter-finals after the unseeded American upset world number eight Tommy Robredo 6-3 7-6.
Novak Djokovic ended Andy Murray's promising run at the tournament when he recovered from a set down to clinch a 1-6 7-5 6-3 victory in the battle of the 19-year-olds.
Murray, who is ranked two places below Djokovic in 19th, made a confident start as he ripped through the first set and looked on course for a place in the quarters after he had broken in the second.
But he faltered just when victory was in his grasp, losing his serve when 4-3 up and allowing Djokovic to recover and level the match. With Murray's concentration broken, the Serb raced away to win the decisive set.
Djokovic will now meet 10th seed Fernando Gonzalez who was given a walkover after Swede Joachim Johansson withdrew because of a throat infection.
ANKLE INJURY
Sixth seed Roddick suffered a 7-6 6-3 defeat at the hand of Berdych with the American ending the match complaining of pain in his left ankle.
There was better luck for fourth-seeded Argentine David Nalbandian who won a tight contest against Britain's Tim Henman 6-2 2-6 7-5.
The former British number one served for the match, but Nalbandian managed to stage a successful fightback after the two players exchanged words over each other's service calls.
"It's frustrating but there were a lot of tight points in those last few games," said Henman. "He questioned my sportsmanship, but if we go down that road there is only going to be one winner."
Marat Safin, winner in Madrid in 2004 but unable to defend his title last year because of injury, had few problems seeing off Kristof Vliegen of Belgium 6-3 6-2 and now meets Nalbandian.
