Max Christie’s side, who couldn’t name a player on the bench due to injury, went a goal down early on but struck twice in the second half through Nick Locke and Kieran Mitchell to seal a chance to take home the trophy next weekend in the capital against East Kilbride.
The first real chance fell to on-form loan star Kieran Offord, who was played in one-on-one against Bo’ness ‘keeper Andy Murphy by Jack Hodge.
However, the St Mirren man fired a low effort wide of the target when it looked easier to score.
Bo’ness had their first shot on goal 13 minutes into the tie when Dundee United loanee Lennon Walker tested Ross Connelly from range, but the Shire stopper was equal to it.
Full-back Dylan MacDonald was having a good game down the right side and his delivery was causing problems for the Bo’ness backline.
The hosts took a deserved lead on the half hour mark when Offord smashed home from a tight angle after being played in by Hodge.
He should have made it two when he found space in behind but Murphy made a superb stop down low to halt him.
Shire were on the hunt for a second and Dean Watson took advantage of a leggy Bo’ness to dart in on goal, only for his chipped effort to crash off the side netting.
Christie’s side, who were led on the day by assistant coach Stuart Hunter, were struggling to make an impact on the match and the hosts poor finishing was the only thing keeping the score down going into the break.
However, they could have levelled when Jamie McCormack broke the outside trap and forced Connelly into an excellent diving save.
Gregor Nicol also had an effort one-on-one saved as the away side finally came to life.
In the second half the hosts were once again the quick starters, with Hodge and Barr both having efforts at goal.
But it would be Bo’ness to score next and bring themselves back into the semi-final with a wonderful free-kick on 57 minutes from Nick Locke.
After a handball just outside the area, the midfielder struck the ball into the top corner with a pinpoint effort to level the tie.
On the hour mark the match was turned on its head when the away side took the lead, with Shire falling to pieces.
Nicol was given all the space in the world to drive forward and feed in Mitchell who fired home into the far corner.
With a cup final on the line the match turned into a real scrap, with Watson and Johnston going in the book for each side after poor challenges.
McCormack made an acrobatic goal-line clearance as the hosts looked to get into the match, but they looked down and out.
Centre-back Tyler Futon had a tame header deflected wide as Bo’ness looked set to hold on to their slim lead with only minutes left.
In injury time McCormack took one for the team as he hauled down Offord who was through one-on-one to keep the score level. The combative defender was sent off for his troubles as Bo’ness finished the match with ten men.
The final will take place at Ainslie Park next Sunday afternoon, with kick-off in Edinburgh at 3pm.
East Stirlingshire: Ross Connelly, Dylan MacDonald, Cameron Crooks, Tyler Fulton, Connor Greene, Jack Hodge, Kenny Barr, Andy Kay, Kieran Offord, Jamie Hamilton, Dean Watson.
Subs: Blair Sneddon, Andy Shirra, Adam Mansouri, Craig Henderson, Kieran Gibbons, Iain Ure.
Bo’ness United: Andy Murphy, Jamie McCormack, Ryan Stevenson, Greg Skinner, Michael Gemmell, Gregor Nicol, Keiran Mitchell, Nick Locke, Keir Macauley, Kyle Johnston, Lennon Walker.
Subs: No one on bench.