Hamilton got the second half underway, and straight away looked like carrying on where they left off.
Callum Douglas was put through on goal again by strike partner David Thomson, and when the forward was brought down by Celtic 'keeper Sean Baxter, many around the pitch were calling for the red card.
Fortunately for Baxter, the referee deemed the foul as only a yellow card.
From the resulting free-kick, right-back Dean Burton fired a low drive whistling just past the bottom left post.
Hamilton should have found themselves a goal up for definite when Connor Burns had a free header from another wonderful corner by Connor Smith. Burns could only head just wide, though it's doubtful whether the midfielder expected the ball to find it's way straight through to him.
Celtic carved out a good opportunity at the other end with Lewis Cameron also nodding the ball narrowly past the post from a nice ball in by Anthony Coutts.
Hamilton finally broke the deadlock and frontman David Thomson got a well-deserved goal after some brilliant pressing play.
Thomson tore around the Celtic defence like a terrier, putting pressure on the defenders and eventually winning the ball. After doing so, some nice footwork and a clever touch to the side created the angle for a deadly effort high into the top left corner.
Celtic found themselves back level after winning a penalty only minutes later.
Lewis Cameron was brought down in the box and Jamie Mulligan stepped up to send the keeper the wrong way, slotting the ball into the bottom left corner.
Celtic couldn't consolidate and capitalise on the leveller though, and we saw the third goal goal in ten minutes soon after their goal.
Callum Douglas got the goal this time, slotting past Sean Baxter and sending the Accies into dreamland.
After that, it was just a case of keep-ball for Hamilton.
They ended the match just as they started it though, creating yet another chance to extend the lead. A lovely one-two between Fraser McLennan and David Thomson saw Thomson shoot just wide for what felt like the hundredth time in the game.
The Accies fully deserved to book their place in the Semis and should be one to watch on the road to Airdrie.