The Clarets have been out of the top flight since 2010, but first-half goals from Ashley Barnes and Michael Kightly ensured that the likes of Liverpool, Manchester United and Chelsea will all be visiting Turf Moor next term.
After a slow start to the contest, the hosts took the lead in the 22nd minute. Dean Marney was the creator, crossing for Barnes to convert with an instant finish.
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Up the other end, Marc-Antoine Fortune hit the crossbar with a header and Burnley went on to make the most of their good fortune three minutes before the break.
From the left flank, Kightly's powerful cross evaded everybody as the ball crept inside Ali Al Habsi's far post.
As the match drew to a close, Emmerson Boyce went close to reducing the arrears, but he headed wide and with it went Wigan's last meaningful effort.