A Mark McLaughlin header in the final moments of the first half was enough to see the home side through.
Livi manager Gary Bollan said: “The players are really down as cup final appearances do not come along too often. We created chances, and Iain Russell is pretty devastated as he is usually our Mr Reliable in front of goal.”
Livi started brightly, with Russell and Kenny Deuchar linking up to cause problems for the Hamilton defence. As the half wore on, however, Hamilton began to cause problems. Andy McNeil was twice called on as long-range efforts threatened to find the net, before Accies snatched the lead.
A corner was swung in from the right and Livi failed to deal with it as the ball was nodded back across the six-yard box for McLaughlin to head home from three yards out.
The goal was a blow to the Lions, who had arguably had the better of the first half, and they had two opportunities to get back level on the stroke of half-time.
Firstly, Russell found himself played through from a Deuchar flick-on, but Tomas Cerny foiled the striker’s powerful effort at the near post. Stefan Scougall and Liam Fox then got in each other’s way and neither could muster an effort on target.
The second period saw Hamilton begin to tighten their grip on the game, but Livi still had chances. Deuchar had a header at the back post go over the bar, while Sinclair saw his free-kick held by Cerny. Russell was then handed a golden chance in stoppage time, but after being played one-on-one with Cerny he lobbed the ball clear of both keeper and bar.
Accies will meet Falkirk in the final after the Bairns beat Annan Athletic 3-0 at Galabank.