The Paolites showed determination to overturn an early deficit, with Moritz Römling and Joseph Mbong scoring the goals that sealed a crucial victory and confirmed their qualification for the championship section.
Balzan made the brighter start and took the lead in the 13th minute when Dimeji Awosanya capitalised on a defensive mistake to put his side ahead.
Hibernians responded almost immediately, with Römling striking the upright just three minutes later. Balzan continued to threaten and could have doubled their advantage before the interval, but goalkeeper Matteo Cardinali produced an important save to deny Awosanya.
The second half brought a dramatic turnaround as Römling equalized for Hibs in the 51st minute with a close-range finish.
The match then took another unexpected twist when Joy Mickels appeared to have given Hibernians the lead. However, following a review by the Football Video Support system, referee Daniel Casha disallowed the goal and awarded Balzan a penalty for an earlier infringement.
Awosanya stepped up to take the spot-kick, but Cardinali produced a decisive save to keep Hibernians level.
That save proved crucial as the Paolites were awarded a penalty of their own minutes later, with Joseph Mbong making no mistake from the spot to complete the comeback.
Hibernians successfully defended their narrow advantage during the closing stages to claim three valuable points.
The victory lifted Hibernians to 16 points and secured their place among the top six teams, continuing their recent improvement with a third victory in four matches.
The result also ended Birkirkara's hopes of qualifying for the Top Six after the Stripes were held to a 2-2 draw by Birżebbuġa St Peter's.
Meanwhile, Balzan finished their Opening Round league-phase commitments on 11 points and will compete in the Bottom Six.
Hibernians now join Valletta, Sliema Wanderers, Ħamrun Spartans, Marsaxlokk and Floriana in the championship section.
Final score: Balzan 1–2 Hibernians
Scorers: Dimeji Awosanya (13') for Balzan; Moritz Römling (51') and Joseph Mbong (penalty) for Hibernians.