Tomic ousted Granollers, seeded eighth, 6-3, 6-0 in 59 minutes. Tomic fought off seven of the eight break points he saw in the first set and then didn't allow Granollers a break chance in the second for a win that completed first-round play of the event.
Tomic lost only two of his 14 points on serve in the second set while piling up three breaks and taking 12-of-16 of the points when Granollers served.
Tomic won the first title of his ATP career last year in Sydney.
No. 7-seeded Marin Cilic got by qualifier Jan-Lennard Struff 3-6, 6-3, 6-3. Cilic lost the only break point in the first set but didn't lose his serve after that.
Albert Ramos, taking the place of injured fifth-seeded Vasek Pospisil, came out ahead 4-6, 6-3, 6-4 over Sam Querrey. Querrey had 16 aces and fought off 11 of the 14 break points from Ramos but could only solve Ramos' serve once.
Other players advancing to the second round Tuesday were Nicolas Mahut, Sergiy Stakhovsky, Blaz Kavcic and Alexandr Dolgopolov.