The Italian teenager eventually prevailed 6-4 3-6 7-6 (7-3) on Sunday (AEDT) after two hours and 15 minutes on court in the Bulgarian capital.
Pospisil sent down 14 aces as he fought back impressively after losing the first set, the Canadian emphatically overcoming an early break of his serve in the second to level up proceedings.
There was little to split the pair in the decider, Sinner seizing the advantage in a tense tie-break when he forced a pair of errors out of his opponent and grasping his chance to be crowned champion.
At 19, Sinner becomes the youngest champion on the ATP Tour since an 18-year-old Kei Nishikori at the Delray Beach Open back in 2008.
He is also the youngest player from Italy to triumph at an event in the Open era, finishing a breakthrough 2020 season with an impressive 19-11 record.