Bay created good chances late on with captain Bill Robertson twice heading wide, Harry Edge and Tom Doyle doing likewise, and Sean Lovemore shooting just wide then coming tantalisingly close with a shot that brought out a brilliant reaction save from All White stopper Jacob Spoonley.
Predictably, their late charge left them open at the back, and Justin Gulley - who had tormented Bay all afternoon with his charging runs - took advantage of the space to rifle past Andy McNeil in injury time.
A dejected Greatholder afterwards said his troops fought valiantly but were up against a strong opposition.
"We deserved to edge the game, and I don't think we deserved to lose last week either, but they defended well and all credit to them, they had a first-leg advantage and wanted to defend that with their lives.
"We didn't move the ball around as well as we could have at times, but we did put them under pressure and we've created about seven or eight decent chances but today is the day we just haven't scored the goals we've needed."
Bizarrely, Greatholder felt the dismissal of Peverley helped Wellington more than Bay Utd.
"It forced them to stay behind the ball and to counter, and the longer it went on the more we needed to take more chances and that opened us up at the end, which is tough on the lads."
However, by the time Gulley scored the sole goal, Bay were already out as there wasn't time to snatch two late goals.
The result left Wellington coach Matt Calcott elated and he couldn't resist sticking the knife in. "There was a lot of talk about Hawke's Bay coming here and beating us but that is five times we have beaten them this season. And, you know, everything they've thrown at us in those games we've dealt with.
"To deal with that many balls that they've delivered into the box is absolutely outstanding."
Referring to a long-running dispute between the sides Calcott said his side kept their focus on events on the pitch.
"We deserve to be in the final, we've had a lot of stuff flung at us off the pitch from Hawke's Bay recently and we've just kept our mouth shut and got on with the job."
Wellington now play Auckland City in this weekend's grand final in Auckland after the latter thrashed Waitakere United 4-1 in the second leg of their semifinal.