The Lilywhites got off to a dream start when Josh Whittam pounced on a goalkeeping error to put the home side in front after just five minutes.
The seasiders went on to create a number of chances during the rest of the first half, but failed to add to their one goal.
After the break, Kirton came more into the game, and Skegness keeper Ashley Bentley made a string of fine saves to keep the lead intact.
The visitors finally equalised 15 minutes from the end to take the game into extra time.
Further goals in the 91st and 119th minutes secured Kirton’s place in the final.
Town: Bentley, Booth, Tipper, Forman, James Whittam, Cotterill, Pearce, Rasmussen, Josh Whittam, Miller, Pellow, Wathall, Rawlinson, Clark.
Skegness Town Reserves are in action next on April 30, when Old Leake will be the visitors to Burgh Road in the Boston premier division, with a 2.30pm kick-off.
They will wrap their season up on May 7 when they host neighbours Spilsby Town, with a 2.30pm kick off.