The Bank of Ireland Senior Cup has been won by either Ballynahinch or Armagh for the past five seasons - but now they will meet in the final for the first time at the Kingspan Stadium on Friday, March 6.
In the semi-finals, holders Armagh eliminated Rainey 28-18 at Magherafelt, while Hinch beat Dungannon 30-21 at home.
Rainey took the lead against Armagh with an Andy Magrath try, converted by Martin Connolly, before the visitors' Cormac Fox kicked his first penalty.
Connolly cancelled that out but Armagh struck back to take an 11-10 interval lead with winger Josh Morton squeezing over followed by a second Fox penalty.
Rainey regained the advantage with another Connolly penalty but from then on the visitors held the upper hand with tries from Nigel Simpson and Andrew Willis. Fox converted both and kicked another penalty, while Andrew Donaghy grabbed a consolation home try.
Elsewhere, Hinch went in front after Aaron Cairns cut through for Greg Hutley to convert before a long-range counter by Hutley and Paddy Wright resulted in a Ryan Wilson score.
Poor defending allowed the visitors back into the tie with a Malcolm try followed by one from Andrew McGregor for Jordan McIlwaine to convert both.
Hinch forged to a 30-14 lead before Dungannon bagged a late converted score.