Del Potro seemed to be in control of the first set, was a break up and after Baghdatis managed to force a tiebreak, the Argentinian had two set points, but couldn’t convert them.
In the second set, Baghdatis broke Del Potro in the 7th game of the second set and served out the match.
The 2010 champion Baghdatis will now play Julien Benneteau in the semis. Benneteau beat Russia’s Alex Bogomolov Jnr. 6-2, 6-4.
In the other quarterfinal, Denis Istomin of Uzbekistan upset the Frenchman Richard Gasguet, beating him 6-4, 7-6 (7-4). He will now face the Finn Jarkko Nieminen, who eliminated Bobby Reynolds of America 6-3 6-3.