Djokovic broke Baghdatis once in each set and that was enough for him to wrap up the match.
He will face fellow Serbian Viktor Troicki in round three. Troicki had to fight harder for his victory over the Spanish qualifier Guillermo Garcia-Lopez as he beat him 4-6 6-1 6-4.
Also through to the third round is the 11th seed Argentine Juan Martin del Potro, who defeated the big serving Ivo Karlovic of Croatia in straight sets 7-5 6-4.
Del Potro’s next opponent will be the Croat Marin Cilic, who dismissed Igor Kunitsyn of Russia 6-3 7-6 (1).
The no.5 seed David Ferrer beat the Australian Bernard Tomic 6-4 6-4, who could get a possible fine for coaching. When interviewed, Tomic said he only asked his coach (father) John to restring some of his rackets.
In the other matches, Albert Ramos won against his fellow no.15 seed Spaniard Feliciano Lopez 6-4 7-6 (5), French Richard Gasguet overcame Cedrik-Marcel Stebe of Germany 6-3 6-7 (6) 6-2, no.12 seed Nicolas Almagro beat the Belgian qualifier David Goffin 6-4 6-2 and Julien Benneteau of France battled past Benjamin Becker of Germany, winning 3-6 6-3 7-6 (4).