The 21-year-old Australian, who took the title in 2013 but is unseeded for this year’s event, dispatched his Spanish opponent in under an hour.
Granollers did manage to fashion eight break-point opportunities but Tomic saved seven of them while breaking his opponent’s serve on five occasions.
Elsewhere in Sydney, Seventh seed Marin Cilic battled his way into round two with a 3-6 6-3 6-3 victory over German qualifier Jan-Lennard Struff.
Nicolas Mahut will face top seed Juan Martin del Potro in the second round after the Frenchman edged America’s Ryan Harrison 7-6 (7-2) 7-5.
Home hope Marinko Matosevic progressed after a 6-2 4-6 6-3 win over Florian Mayer, but fellow Australian Samuel Groth was beaten 6-7 (6-8) 7-6 (7-5) 6-2 by Radek Stepanek.
There were also first-round victories for Alexandr Dolgopolov, Albert Ramos, Blaz Kavcic and Sergiy Stakhovsky on Tuesday.