They scored 29 unanswered points in the second half to dethrone the holders and secure the Cup for the first time since 2017.
A Greg Hutley penalty had given them the lead on the day, before QUB hit back through Johnny Hunter who showed incredible pace to outrun the defence and touch down right of the posts.
Hinch then had Mark Best shown a yellow card for a deliberate knock-on and Queen's immediately took advantage with the backs combining well before Michael Orr finished in the corner, with Ritchie McMaster converting.
He then added another penalty to give them a 15-3 lead at the half in their efforts to retain the Bank of Ireland Senior Cup.
HT Ballynahinch 3-15 QUB
Hinch came out a much-changed side in the second period, and captain Bradley Luney looked almost certain to score before Rory Telfer held him up over the line.
It was then QUB's turn to receive a yellow card, with scrum-half James Wright sent to the bin for going off his feet at the breakdown.
This time it was Hinch who made the numbers count with Hutley slinging the ball wide for Aaron Cairns to dive into the corner and score to spark the comeback. Hutley then added the extras to make it 15-10, and soon slotted a penalty to further reduce the deficit.
Hinch then recovered the ball from the restart through Luney and got themselves in front for the first time in the final. Replacement John Charles found Zac McCall, and the blindside flanker broke through a couple of tackles on his way over the line to make it 18-15.
QUB tried to battle back into the game, but Reuben Crothers won a big turnover for Hinch close to their own line, and then Queen's lock Jake McCay saw yellow for a deliberate knock on.
Again Ballynahinch made the numbers count, and after a line out maul, Best hit the line on the full and crashed over to score a vital try in the corner, with Hutley nailing a tough kick to make it 25-15.
Hutley then made sure of the win with a great piece of opportunistic finishing. As the ball broke loose from a ruck in the QUB 22, he grubbered it towards the whitewash, before chasing it down and diving in to score.
He stepped up and slotted his kick to ensure Hinch couldn't be caught, and they won the Bank of Ireland Senior Cup for the first time since 2017.
### Team Lineups
Ballynahinch
15-9: Ethan Graham; Fergus Jemphrey; Ryan Wilson; Mark Best; Aaron Cairns; Greg Hutley; Conor McKee
1-8: Nacho Caldera; Claytan Milligan; Kyle McCall; James Simpson; Tom Martin; Zac McCall; Reuben Crothers; Bradley Luney (C)
Replacements: Josh Hanlon; Joe Charles; Kyle Gill; Chris Gibson; Jack Milligan
Queen's University Belfast
15-9: Rory Telfer; Michael Orr; Robbie Johnston; Ben Power; Jonny Hunter; Ritchie McMaster; James Wright
1-8: Jack Boal; Alexander Clarke; Matthew Miller; Joe Hopes; Jake McCay; Lorcan McLoughlin; Curtis Pollock; David Whitten (C)
Replacements: Harry Long; Niall Carville; Gary Dillon; Harry Patterson; Ben Heath