Britain's Andy Murray and Serbian Novak Djokovic both suffered defeats to American opponents with Mardy Fish and Andy Roddick advancing to meet each other on Saturday.
The only member of the top four to progress was third-seed Roger Federer, who meets a confident Baghdatis for a spot in Sunday's final after defeating Russian Nikolay Davydenko 6-4, 7-5.
Nadal was well below his best against an inspired Baghdatis, whose big serve was on full power - he blasted 18 aces while the Spaniard could manage just four.
An All-American semifinal is a timely boost for the game in the US which is currently without a top ten male player -- although Roddick's win assures he is back to at least ninth in next week's rankings.
Roddick and Fish are close friends who, since their high school days, have spent many hours together practicing. Roddick beat third-ranked Serb Djokovic 6-4, 7-5, his booming serve looking back to its best. Fish took advantage of an exhausted world number four Murray, who wilted in 100-degree heat (38 Celsius) and lost 6-7, 6-1, 7-6 to the unseeded American.
Bhupathi-Mirnyi in semis
India’s Mahesh Bhupathi and Max Mirnyi of Belarus defeated Poles Mariusz Fyrstenberg and Marcin Matkowski 6-3, 6-2 and advanced to the doubles semifinals . They will meet fifth seeds Austrians Lukasz Kubot and Oliver Marach who beat Cezch Republic’s Frantisek Cermak and Slovakia’s Michal Mertinak with a 6-4, 6-2 win in 75 minutes.
Clijsters injured
An injured Kim Clijsters hobbled to a 2-6, 6-3, 6-2 quarterfinal loss to Vera Zvonareva at the Montreal Cup, casting doubt on the Belgian's ability to defend her US Open crown.
World number two Caroline Wozniacki blasted her way into the semifinals with a 6-3, 6-2 win over French Open champion Francesca Schiavone of Italy.
Wozniacki will next face in-form Russian Svetlana Kuznetsova, who scored a 6-1, 6-3 win over China's Zheng Jie. The other semifinal will pit Zvonareva against Victoria Azarenka of Belarus, who moved on with a 6-2, 7-6 win over Frenchwoman Marion Bartoli.