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It was a tense battle between the two sides, both of whom had roaring support in the Wembley crowd, but chances were few and far between in the early stages of the match.
Wimbledon came closest to scoring inside the opening 10 minutes when the ball was headed across goal, but Taylor's flick from eight yards out did little to trouble goalkeeper Luke McCormick.
At the other end, Graham Carey tried to find the breakthrough with a 35-yard shot for Plymouth, but there was too much flight on the ball and it flew over the crossbar.
Wimbledon had a decent spell of pressure in the first half as a block from Kelvin Mellor was needed to deny a shot from Andy Barcham, while Callum Kennedy attempted to fire home from 30 yards out, but McCormick managed to catch the ball.
After the half-time break, Carl McHugh almost sent the ball into his own net after looping it back to the keeper, but his touch was heavy and missed McCormick, who watched the ball bobble slightly wide of the post.
After surviving the gaffe, Plymouth were on the back foot when Taylor charged down the left-hand side before delivering a cross into the danger area.
A few minutes later, Plymouth had an opportunity to strike from a set piece as Carey lined up a free kick in a dangerous position, but his attempt was scrambled away by goalkeeper Kelle Roos.
That 65th-minute free kick was Plymouth's first effort on target, and they were left to rue the missed opportunity as Wimbledon later took the lead.
With 11 minutes of normal time left on the clock, Kennedy whipped the ball into the box from the right-hand side to find Taylor, who skilfully flicked it into the far corner.
Barry Fuller should have made it 2-0 in the closing stages of the match, but his attempt from close range was denied by the keeper.
During stoppage time, which was indicted as seven minutes, Plymouth tried to force the match into extra time with an equaliser, but they ran out of ideas.
As it turned out, Akinfenwa hammered the final nail in the coffin when he slotted home a penalty seconds before the final whistle.