The shock defeat will reopen the debate about the Madrid Open's use of blue clay.
Spaniards Antonio and German Garrido took the Madrid Open title in 1977 and 1973 respectively.
Meanwhile, world number two Novak Djokovic pulled out of the Madrid Open on Saturday due to continued breathing problems.
Djokovic is expected to defend his title at the Madrid Open next month ahead of the second grand slam of the season in Paris.
Edfors, whose previous best performance on the European Tour was a tie for ninth at the Madrid Open in 2004, now has a two-year exemption.
The clay court season now looks towards the start of the Madrid Open on Monday, which has caused controversy over its use of blue clay for the first time.
Sharapova has only been beaten once on clay all season, in the Madrid Open final, and has taken titles in both Stuttgart and Rome leading into the tournament in Paris.
The 31-year-old will take nearly two months off after the BNP Paribas Open in Indian Wells, which runs from March 4-17, before returning in May to play the Madrid Open.
His triumph this year came after the Olympic champion suffered a surprise early exit, although he had earlier ended Nadal's 33-match winning streak on clay in the Madrid Open final.
Murray arrived in Russia having sealed back-to-back Masters Series titles in Cincinnati and, last week, Madrid, after reaching the US Open final in between.
Wales' Rhys Davies, who won his maiden European Tour event in Morocco in March and had consecutive runner-up finishes at the Madrid Masters and Celtic Manor Wales Open, improved on his opening 78 with a one-under 70 to go into the weekend at six over.
Up to a million people are expected to attend Sunday's open-air mass in Madrid, where two priests and three nuns are to be canonised.
Williams won the Madrid title last week and next faces French Open champion Li Na of China.
Nadal lost the Madrid final and then lost in the French Open fourth round that year, his only defeat in Paris.
With the clay court season about to kick off, Djokovic is keen not to take any unnecessary risks ahead of the Masters events in Madrid and Rome before going into the French Open next month.
Nadal's victory here last year came in Djokovic's absence, and the Spaniard subsequently lost to him in Madrid and Rome before beating Roger Federer in the French Open final for a record-equaling sixth title at Roland Garros.
He covered Spain's 2010 World Cup victory from Madrid and has broadcast live from Wimbledon, the US Open (both tennis and golf), the Ryder Cup, the Open Championship, the Rugby World Cup, the Tour de France, the Abu Dhabi Grand Prix and five consecutive Champions League finals.
Baltacha will play qualifying for Rome and Madrid before taking her place in the main draw of the French Open.
The tour said they expected Roddick to return to action for the Madrid Masters on May 9, which is two weeks before the French Open.
The Madrid side were trying to use playmakers Jose Antonio Reyes and Maxi Rodriguez to open up Bolton but, more often than not, the brave Andy O'Brien and Gary Cahill were quick to block the supply.
After tournament victories in Cincinnati, Madrid and St Petersburg, and with a first Grand Slam final at the US Open in between, Murray had finally begun to show signs of a dip in form this week.
The bombings of four Madrid commuter trains that killed 191 people in 2004 led to tighter security in public spaces and open-air events.
Any Americans still uncomfortable on the red clay will feel more at home: For the first time, Madrid will be using blue clay, much like the color of the U.S. Open courts.
The pair are set to lock horns again at the Madrid Masters which starts next weekend as the build-up continues to next month's French Open where Nadal will be defending his crown.
The virus affecting Del Potro had prompted the tall right-hander to miss recent tournaments in Portugal and Madrid, and he returned in Italy with the hope of being able to compete at the French Open.
Before facing Spain in September, the next big test for the U.S. singles players comes next month in Madrid, where all the world's best men and women will gather on clay for the crucial French Open prelude.
The Spaniard, who won the Open three times and the Masters twice, was admitted to hospital in early October after fainting at Madrid Airport, and subsequently underwent a six-and-a-half hour procedure on 24 October to remove the tumour.
That analysis may be right, to judge by a recent open-air assembly on the economy, with a few dozen participants squatting on the paving stones of Madrid's Plaza del Carmen.
One of the biggest undertakings would be a 17, 800-bed Olympic Village, designed in an "open-air museum" concept, which would "be fully financed and guaranteed by the City of Madrid" to ensure "minimum risk factor, " according to the city's application, submitted in February.
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