The seventh seed proved too strong for the 81st-ranked Dutchman with a 6-1, 6-4, 6-4 victory in just over two hours under the closed roof of the Hisense Arena.
It maintained the 27-year-old American's record of never have lost in the opening round here in nine Australian Opens.
Roddick, who is a four-time semi-finalist in Melbourne, needed just one match point to get past De Bakker, who was making only his second Grand Slam appearance.
Roddick is now 6-0 for the new season after coming into the Australian Open as the winner of the lead-up Brisbane International tournament.
The power-server, whose fastest serve was clocked at 217 kph (135 mph), broke the Dutchman twice in the opening set, which played with the stadium's roof open.
There was a 40-minute rain interruption midway through the second set at 2-2 and the roof was closed, then Roddick grabbed a service break in the seventh game and had three set points saved before he took out the set.
De Bakker, who out-hit Roddick 43-25 winners, got the fourth and final service break in the ninth game of the third set and served out for the victory.
Roddick will play either Teimuraz Gabashvili of Russia or Brazilian Thomaz Bellucci in the next round on Wednesday.