The Cypriot broke his opponent four times throughout the match and was rock solid on his own serve.
Baghdatis will face a tough challenge in round two, he will play world no.1 Djokovic.
Also through to the second round is the big serving Croatian Ivo Karlovic, who overcame Poland’s Lukasz Kubot in a three hour battle, winning 6-3 6-7 (2) 7-6 (2).
Next up for Karlovic will be the 11th seed Argentine Del Potro.
In the other matches, 19 year old American Ryan Harrison turned his match around against Potito Starace, winning 6-7 (6) 6-4 6-4, Australian Bernard Tomic overcame Sergiy Stakhovsky of Ukraine in straight sets 7-6 (4) 6-3 and the Ukrainian qualifier Sergei Bubka beat Ernest Gulbis of Latvia 6-4 6-4.