The success meant they reached 50 points - the first time in 50 years they have achieved their half-century in English football's top-flight.
Birmingham City 2-1 Burnley: As it happened
Burnley were poor opposition and obviously resigned to their fate as first-half goals from Cameron Jerome and Christien Benitez put Birmingham in the driving seat as they increased their unbeaten home run to 14 games.
But Birmingham's lack of real goalscoring power was exemplified in only the second minute of the game when Lee Bowyer miserably failed to score from close range following Jerome's cross.
Jerome himself could have done better himself when he guided a Sebastian Larsson corner over the bar.
Birmingham had another opportunity to go ahead when Jerome watched goalkeeper Brian Jensen flick another close-range header over the bar.
An early goal could have signalled a Burnley collapse. Instead they were able to battle and stay in the match as Birmingham failed to capitalise on their superior play.
The result was that Burnley were given unexpected encouragement to take the game to Birmingham and Jack Cort displayed some confidence with a long-range shot which was handled without any trouble by goalkeeper Joe Hart.
Hart certainly had a quieter game than in the previous match against Villa Park when he displayed his top-flight credentials.
In the 30th minute, however, Birmingham were finally rewarded with a goal, although it was a scrambled affair.
Bowyer headed on Larsson's cross and Jerome forced the ball over the line despite the efforts of Jensen to keep it out.
Unfortunately the goal gave Burnley the dubious record of equalling Wimbledon's Premier League record of conceding in 26 successive matches.
Four minutes before the break there was something of a milestone when Benitez scored his first goal at St Andrew's to take his tally for the season to four.
It came after a James McFadden free-kick was headed back by Roger Johnson to enable Benitez to nudge the ball over the line.
Leading by two goals enabled Birmingham to take their foot off the gas and as a result Burnley displayed more attacking potential with Steven Fletcher firing just over the bar.
The Clarets took off their strikers, Fletcher and David Nugent, and Birmingham found themselves under late pressure when substitute Steve Thompson coolly slotted home a low cross shot three minutes from time.
Source: PA
