The Brazilian is ranked 27 places below his Spanish counterpart but started confidently to take the first set 6-2.
Verdasco, a quarter-finalist here last season, fought back to take the second set 6-4, but Bellucci held his nerve to take the decider 6-3.
Australian Open quarter-finalist Stanislas Wawrinka overcame a second-set wobble as he booked his place in the second round.
The Swiss looked to be on his way to victory against Spain's Pablo Andujar when he took the first set 7-5 on a tie-break, but his opponent hit back to take the second 6-3 and force a decider.
But Wawrinka regained his focus and proved far too strong as he romped to a 6-0 success in the final set.
Fifth-seed Albert Montanes cruised through his all-Spanish tie with Daniel Gimeno-Traver 6-2 6-1 while Argentina's Juan Monaco beat compatriot Horacio Zeballos 7-5 7-6 (7/3).
Eighth seed Juan Ignacio Chela made an early exit as he was forced to withdraw from his clash with Eduardo Schwank while a set to the good.
Fabio Fognini saw off qualifier Maximo Gonzalez 6-3 6-4, with Pablo Cuevas also securing a straight-sets win as he beat Potito Starace 6-4 6-4.
Carlos Berlocq and Ivan Navarro also progressed while third seed Nicolas Almagro defeated Victor Hanescu 6-3 6-2.
Argentina's Gisela Dulko progressed in the women's draw as the fourth seed eased past Anna Tatishvili 6-3 6-1 but second seed Polona Hercog is out after she was beaten 6-3 4-6 6-3 by Spain's Lourdes Dominguez Lino.
Anabel Medina Garrigues cruised to a 6-2 6-1 success against Karolina Pliskova, who also saw her sister Kristyna eliminated by qualifier Madalina Gojnea.
Silvia Soler Espinosa dumped Jill Craybas out with a 6-1 6-1 win while her fellow qualifier Lesia Tsurenko was leading 6-1 3-2 when Melanie Oudin withdrew from their clash.
Hungarian third seed Greta Arn beat Edina Gallovits-Hall 6-4 6-4 and there were also wins for Laura Pous-Tio, Johanna Larsson and Renata Voracova.
Seventh seed Carla Suarez Navarro beat Sandra Zahlavova 6-4 6-1 but eighth seed Olga Govortsova lost out to Mathilde Johansson of France.