Sean Dyche's men knew victory at home to Wigan would secure a return to the top flight regardless of the result in third-placed Derby County's match with Barnsley.
First-half goals from Ashley Barnes and Michael Kightly proved enough to earn three points, keeping Burnley eight clear of Derby with two games of the season remaining.
A pitch invasion followed the full-time whistle in Burnley's clash with Wigan as home fans showed their appreciation and delight.
Derby were 2-1 winners against relegation-threatened Barnsley, with Jeff Hendrick and Johnny Russell on the scoresheet for Steve McClaren's side.
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