Bellucci, with just one win in five visits to Canada and coming off a first-round loss at Washington, appeared to be the perfect opponent for Djokovic to launch his buildup to the US Open but provided a stiff test for the Serb.
"[The] match could have gone either way, honestly, especially in the second set," Djokovic told reporters after battling Bellucci for an hour and 50 minutes.
"But we both had our chances to break. We got to the tiebreak, which I thought was fair, then it was anybody's game.
"It's the first hard-court match for me from Miami earlier this year in March. It takes a little bit of time to get into the rhythm, get into the groove."
The top seed in Canada for the fifth straight year, Djokovic saved all three break points he faced in a tight opening set.
The Serb, who narrowly missed out on a fourth Canada title last year after losing to Jo-Wilfried Tsonga in the final, also saved two break points in the second as the set went to a tie break, which he quickly took control of and took 7-4 to register his 250th world tour Masters 1000 match win.
Only three players have beaten Djokovic in 2015 - Ivo Karlovic, Roger Federer and Stan Wawrinka.
In first-round action, Tsonga opened his title defence with a 6-4 6-4 win over Croatian teenager Borna Coric in a rain-interrupted match that began on Monday.
South African 12th seed Kevin Anderson was a 7-6(2) 7-6(4) winner over Czech Lukas Rosol while Bulgarian 14th seed Grigor Dimitrov, a semifinalist last year, advanced 6-4 7-5 against Ukrainian qualifier Alexandr Dologopolov.
Belgian 13th seed David Goffin beat American Steve Johnson 6-2 6-2, leaving John Isner to carry the United States flag into the second round, the 16th seed blasting 23 aces past Germany's Benjamin Becker in a 6-4 6-7(6) 6-3 win.
