The seventh-seeded Roddick produced a clinical performance to run out a 6-3 6-4 6-4 winner over the 35th-ranked Brazilian in a little over two hours.
The American's victory was briefly delayed when he challenged a line call on match point while leading 40-15. The ball was deemed to be 'in' and chair umpire Fergus Murphy awarded Bellucci a point, much to Roddick's bemusement.
The big-serving American then produced what he thought was an ace to seal the victory, only for Bellucci to challenge the call.
The Hawk-Eye replay system determined the ball to be 'out', forcing Roddick to make a second serve.
However, Bellucci belted a forehand long in the subsequent rally to finally hand Roddick the win.
The world number seven continued to argue with Murphy afterwards, claiming he could have played the ball on his first match point.
"I was in a position to hit it," Roddick told Murphy. "It's not up to you to make that determination."
(Reporting by Greg Stutchbury; Editing by John O'Brien)