The Clarets began the game at Turf Moor knowing a win would be enough to confirm a top-two finish after Brighton drew 1-1 with Derby earlier in the day.
After an edgy first hour, Sam Vokes headed in Dave Jones' free-kick to seal promotion at the first attempt.
Sean Dyche's side are only two points clear of Middlesbrough and Brighton, but cannot be overhauled by both as they face each other on the final day.
While Boro and Brighton fight for the remaining automatic promotion spot on Saturday, Burnley will be crowned champions if they win at relegated Charlton.
However, the Lancashire side were far from their best against mid-table Rangers and survived a scare when Alejandro Faurlin hit the post with a long-range drive with 20 minutes to play.
How Burnley reached the Premier League
READ MORE: Dyche 'never blinked' in promotion race
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