The Eagles will now play Bristol City in the two-legged play-offs as they attempt to return to English football's top-flight for the first time since 2005.
It has been a magnificent effort by a Palace team that were 19th in the table when Neil Warnock replaced Peter Taylor as manager seven months ago.
The match was effectively over as a contest after only ten minutes as Palace were already two goals ahead by that stage while the Clarets were down to ten men following Clarke Carlisle's red card.
The deadlock was broken in the eighth minute when Carlisle recklessly brought down Scott Sinclair. The Burnley player was shown a straight red card before Ben Watson smashed his spot-kick past Brian Jensen.
Two minutes later Palace doubled their lead when Sinclair's jinking run ended with his cross being half-cleared to Jose Miguel Fonte. He headed the ball back into the penalty area for unmarked teenager Victor Moses to fire home.
It was 3-0 eight minutes before the break when Tom Soares turned the ball into the net from close range after Clinton Morrison had created the opening.
Paul Ifill and Morrison had chances after the break to add more goals before Sinclair scored an outstanding fourth just past the hour mark.
The winger, on loan from Chelsea, cut inside Chris McCann before powering a shot past the hapless Jensen.
The rampant Eagles always looked likely to score a hatful of goals and they made it 5-0 in the 65th minute when Morrison grabbed his first goal of the afternoon.
Watson was the creator, toying with the Burnley defence before finding the former Birmingham City striker who had no trouble finding the net with a strike from just inside the penalty area.