Billy Reid's men thoroughly deserved their win in front of a 2,627 crowd on a crisp Tuesday night, which advanced them through to the quarter-finals at the expense of an ordinary-looking Killie.
Accies stunned their visitors by going 2-0 up inside the first half.
After sixteen minutes David Winters darted past Simon Ford on the right flank and swung in a cross which was badly dealt with by David Lilley.
Young James McCarthy pounced on the loose ball and drilled low past the helpless Alan Combe.
Hamilton then weathered a storm that resembled the Alamo at times, albeit without Killie ever really threatening.
But Accie deservedly scored a second on 37 minutes when Mark Gilhaney's cross from the left was knocked out of the box by Allan Johnston and midfielder James McArthur drilled an unstoppable shot into the bottom left corner.
Winters nearly increased Hamilton's tally a minute latter but Combe superbly blocked his close range shot and Ford blocked the striker's rebound.
Winters also latched on to a defensive error after 25 minutes but after beating Combe to the ball he could only find the side-netting.
Killie's best chance fell to Johnston in the 33rd minute when he sent a volley flashing past the bottom left corner after Lilley's corner was poorly defended.
The second half was played at a slower pace and it took until the 68th minute for either side to register a decent shot on goal.
Again that fell to Hamilton with Winters seeing a neat curling effort held at the right post.
Killie substitute David Fernandez made his side's task more difficult in 78 minutes, collecting two needless bookings inside 60 seconds and receiving his marching orders from referee Kenny Clark.
Goalkeeper Combe kept his side in the game in the 8st minute with a stunning save form Brian Wake's point-blank volley.
Combe was called into action two minutes later when he superbly pushed Gilhaney's net-bound drive away from the top right corner.
Wake nearly wrapped up the win after 88 minutes but sent his curling effort inches past the post.