The Adelaide-born former world number one was cheered on by a home crowd as he beat his German opponent 7-5 6-4 3-6 7-5.
Speaking after his victory, 30-year-old Hewitt revealed that his fans helped him advance to round two.
"Yeah, [the support was] fantastic," said Hewitt. "The crowd really lifted towards the end of the fourth set there when I started to get back into that set.
"Feelings like that you can't buy. Until you're one of the players out there experiencing it ... it is a massive adrenaline rush."
Hewitt will take on America's Andy Roddick in the next round.