Fleetwood won a tense game when Burton goalkeeper Dean Lyness misjudged the flight of Antoni Sarcevic's 30-metre free-kick 15 minutes from time and although he got a hand to the ball, he could not stop it flying into the net.
The club, based on the North West coast of England and nicknamed "The Cod Army", played in the minor leagues from their formation in 1908 until they won promotion to League Two in 2012.
They finished 13th in their first League season a year ago and were fourth this season behind the promoted trio of Chesterfield, Scunthorpe United and Rochdale and have now completed their sixth promotion in 10 seasons.
The match was the final game of the domestic English season following Queens Park Rangers' 1-0 win over Derby County in the Championship playoff at Wembley on Saturday and Rotherham United's penalty shootout win over Leyton Orient in the League One playoff final there on Sunday.
(Reporting by Mike Collett, editing by Pritha Sarkar)
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