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Fleetwood started much the more positive of the two sides at Wembley, with two chances falling to David Ball within the opening three minutes. Lyness was on hand to tip the striker's first effort over the crossbar, before the stopper shovelled a header from the same player away from danger.
The Cod Army continued that domination throughout the half, but they were unable to turn possession into goals, while up the other end Burton couldn't call Fleetwood goalkeeper Chris Maxwell into any meaningful action.
Just 40 seconds after the restart Ball had another opportunity to put Fleetwood into the lead, but he was off balance as he attempted to lob Lyness, who collected with ease.
Then, in what was a rare venture into the Fleetwood area in the 71st minute, Burton defender Shane Cansdell-Sherriff evaded his marker to meet Alex MacDonald's corner, but just when it looked as though a goal was inevitable, Cansdell-Sherriff failed to make contact with the ball and the chance passed by.
The decisive moment occurred only four minutes later as Antoni Sarcevic was credited with the goal, although Fleetwood received a big help from Lyness. He misjudged the flight of the ball from Sarcevic's intended cross from wide on the left and, despite his despairing stretch, the ball brushed his hand on its way into an unguarded net.
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As the clock ticked down Burton committed virtually their whole team forward in search of an equalising goal, but despite a number of dangerous moments, Fleetwood held firm to ensure it would be them that will play their football in England's third tier next year.