The 26-year-old Baghdatis recovered from a set down to reach his fourth quarterfinal in 2012.
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Martinez fielded sides stocked with reserves and fringe players right up until the quarterfinal.
The only Premier League team Wigan eliminated was Everton, beaten 3-0 in the quarterfinal.
On Friday, UEFA, European soccer's governing body, drew the quarterfinal match-ups for the 2012-2013 Champions League.
Elsewhere, the American men's volleyball team was knocked out by Italy in the quarterfinal.
Meanwhile, sixth seed Tomas Berdych sealed a quarterfinal place with a 7-6 7-5 win over Kevin Anderson.
Ivanovic, the 2008 Indian Wells winner, beat French seventh seed Marion Bartoli 6-3 6-4 in their quarterfinal.
When she took the match, earning her first quarterfinal seat in a Grand Slam, the room exploded.
Tuesday's other quarterfinal will be between German 10th seed Angelique Kerber and Italy's No. 21 Sara Errani.
Home favorite Andy Roddick, playing in his final tournament, is looming as a possible quarterfinal opponent for Djokovic.
Nadal will now face France's Jo-Wilfried Tsonga, who saw off Stanislas Wawrinka 2-6 6-3 6-4 in his quarterfinal tie.
She wouldn't reach a Grand Slam quarterfinal again until the 2011 French Open.
The first quarterfinal match will be played on Friday, when African champions TP Mazembe face Asian champions Pohang Steelers.
Portugal will meet the winner of Saturday's Spain-France quarterfinal Wednesday in Donetsk, Ukraine.
WSJ: Euro 2012: Cristiano Ronaldo, Portugal Show Czech Republic the Exit
Federer is through to his 32nd successive quarterfinal after beating 21-year-old Belgian debutant David Goffin 5-7 7-5 6-2 6-4.
In particular, a quarterfinal berth allows some teams to make a killing, thanks to the three-month window to sell tickets.
Seeded seventh in the league, the Griffins rolled to the title by defeating top-seeded Air Force in the quarterfinal round.
American Christina McHale earned a surprise 6-2 6-4 win over Czech 24th seed and 2007 Australian Open quarterfinal Lucie Safarova.
Then came his two goals against the Netherlands in the final group stage match that sent Portugal into the quarterfinal.
WSJ: Euro 2012: Cristiano Ronaldo, Portugal Show Czech Republic the Exit
Argentina will host France in another quarterfinal after both nations completed 5-0 victories on Sunday, against Germany and Israel respectively.
No matter the outcome of that quarterfinal, it should set up a showdown of two of Europe's most storied soccer nations.
WSJ: Euro 2012: Germany Kicks Greece Out of Euro (Soccer Tournament)
The game was a rematch of a tightly contested Big East quarterfinal last year, won by Cincinnati 72-70 in double overtime.
Fiji nonetheless deserve all the plaudits after contributing hugely to a quarterfinal weekend when the 2007 World Cup finally came alive.
She will play Kaia Kanepi of Estonia in the last eight with the other quarterfinal between Bojana Jovanovski and Petra Martic.
Defending champion Maria Sharapova continued her title defense in style by beating Serena's sister Venus 6-4 6-3 in their quarterfinal clash.
The whole year, he put the ball in the back of the net and look what he did in a quarterfinal game.
Meanwhile, South Korea beat Iran 1-0 in in the later quarterfinal, again after extra-time, to set up a last-four meeting with Japan.
Borussia Dortmund provide a second helping of quarterfinal action on Wednesday evening.
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