The number 24 seed faced a tough battle against his compatriot in the first set, but eventually managed to take one of his four break points to help him secure the set 6-3.
The 22-year-old found his rhythm in the second set and took the attack to Hewitt on his serve, which allowed him to break the veteran twice and help him ease to a 6-2 win.
Hewitt did his utmost to stay in the match in the third set as he raised the level of his game to break Tomic's serve, winning three games in a row to clinch the set 6-3.
Tomic looked to have put the nail in the coffin of his compatriot, but the 34-year-old continued to fight and battled back from staring down the barrel of defeat to break back. Hewitt then secured an important hold to level the scores at 5-5 before he broke again to clinch the fourth set 7-5 to set up a decider.
The players proved to be inseparable in the fifth set as Tomic broke, but was unable to hold as Hewitt hit back at him once more using aggression on his returns. However, the 22-year-old managed to break a second time and served out for the match.
Tomic will face Richard Gasquet in the third round of the competition.