The Brazilian lifted the title here in 2009 and 2012 and he started his bid for a third crown in relatively comfortable fashion, saving all five break points his Belgian opponent fashioned en route to a 6-2 6-3 win.
Bellucci had been in line to face his compatriot Joao Souza in the second round, but that potential showdown became a non-starter when Frenchman Stephane Robert easily beat Souza 6-1 6-4.
Two other former champions were unable to join Bellucci in the next round, though, as Mikhail Youzhny (2013 winner) and Marcel Granollers (2011) were both dumped out.
Seventh seed Pablo Carreno-Busta swept aside Youzhny 6-1 6-2, while Robin Haase was made to work harder by Granollers before claiming a 1-6 7-6 (7/1) 6-4 triumph.
Also on Tuesday, seeded duo Joao Sousa (six) and Santiago Giraldo (eight) progressed with respective wins over Henri Laaksonen and Paolo Lorenzi, while Julian Reister and Marsel Ilhan were also victorious.