Tenth seed David Nalbandian made an early exit, beaten 4-6 6-4 7-5 by fellow Argentine Juan Ignacio Chela .
Waiting for him in the second round will be Spaniard Alex Lopez-Moron or Argentinian Juan Ignacio Chela, both qualifiers.
There were no problems for fourth seed Juan Ignacio Chela who won 6-4 6-3 against German qualifier Tomas Behrend .
Argentina's Juan Ignacio Chela will meet Novak in the last eight after he dispatched Spain's Feliciano Lopez 6-4 6-7 7-6.
Former world number one Carlos Moya and Argentine pair Juan Ignacio Chela and Juan Monaco withdrew earlier in the week with injuries.
Juan Ignacio Chela was leading Paradorn Srichaphan 6-3 3-0 in the first round when the Thai withdrew, and the Argentine meets Briton Andy Murray next.
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Since Andy Murray 's first loss to Juan Ignacio Chela in 2006 Aus Open, 15 sets to 1 and three straight on clay for Murray.
In the other matches Italy's Davide Sanguinetti overcame France's Gregory Carraz 6-3 2-6 7-5, while Robin Soderling of Sweden beat Juan Ignacio Chela, Argentina 6-4 6-3.
After requiring a fairly tortuous rain-hit two days before seeing off Juan Ignacio Chela on Thursday evening, Murray was back on court 20 hours later to face Baghdatis.
In the evening session, Britain's Andy Murray, seeded third showed improved form on clay with a 6-3 6-3 win over Juan Ignacio Chela, his fourth straight win over the Argentine.
Marat Safin earlier beat Juan Ignacio Chela 6-7 7-5 7-5 6-1 in the first match of the day, and Russia now just need to win Saturday's doubles to secure a place in the final.
Spanish 26th seed Marcel Granollers will play Tsonga or Mello if he defeats Portugal's Frederico Gil, while Argentina's world No. 29 Juan Ignacio Chela could face Ferrer if he gets past Spain's Pablo Andujar.
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Argentina's Juan Ignacio Chela completed a 6-0 6-4 7-6 (7-4) victory over American wildcard Ryan Sweeting to set up a possible meeting with Andy Murray - if the Brit can overcome an in-form Richard Gasquet on Monday.
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