Fletcher's first Premier League goal in the 53rd minute broke the deadlock and defender Andre Bikey opened his account for the club nine minutes later.
Midfielder Lee Bowyer spurned Birmingham's best chance in the first half when he missed an open goal from four yards before Sebastian Larsson curled home a consolation free-kick in the fourth minute of stoppage-time.
It was Burnley's first home victory over Birmingham since April 1976 and, having not yet conceded at Turf Moor this season, they are now unbeaten on their own territory since February 28.
For Birmingham, however, it was a fourth defeat in five league matches.
Visiting manager Alex McLeish packed his midfield and, with Burnley playing 4-2-3-1, it meant the middle of the pitch was heavily congested.
A number of niggly fouls did not help the flow of the game and, as a result, there was little football played in the first half - which passed without incident apart from Bowyer's miss.
That came in the 37th minute when Roger Johnson drilled a cross to the far post where the unmarked former Leeds and Newcastle midfielder only had to divert it into an empty net but his body position was all wrong and he knocked it back to where it had come from and Burnley survived.
Neither side deserved to be ahead at the break and it was debatable whether they should have agreed on a point apiece and gone home at half-time.
However, things livened up after the interval as, just three minutes in, half-time substitute Sebastian Larsson blazed over at the far post after being set up by Garry O'Connor.
But it was Burnley who took the lead in the 53rd minute with a quick counter-attack after a Blues free-kick broke down.
Right-back Tyrone Mears carried the ball out of defence, sent Fletcher racing through the inside-left channel and the former Hibernian forward drilled a left-footed shot which deflected off Hart's legs and into the roof of the net.
It was the Scotland international's first Premier League goal and he should have doubled his tally soon after.
Robbie Blake picked him out in the penalty area and he turned Scott Dann and beat Joe Hart, only to see his shot roll against the foot of the post and Birmingham scramble it away.
Full of confidence, Fletcher then forced Hart into a good low save to his right as the balance of play swung decisively in Burnley's favour.
Bikey, playing a holding role in midfield, ensured the hosts would not rue those misses as he created and scored the second in the 62nd minute.
The Cameroon defender won the ball, wriggled past two markers, charged forward to exchange passes with Nugent and shot beyond Hart and into the left corner for his first goal since a summer move from Reading.
McLeish's last throw of the dice was to send on Kevin Phillips for Teemu Tainio with just over 20 minutes to go, while Fletcher was replaced by Chris Eagles to a standing ovation.
Hart had to be at his best to deny Mears' 20-yard free-kick, with Bikey heading the resulting corner over.
Larsson curled in a late free-kick but it was too late as Burnley showed, once again, why Turf Moor will be their battleground as they bid to secure another season in the top flight.