The hosts broke the deadlock 44 minutes into an evenly-matched first half when Tom Ince's speculative low drive took a significant deflection off Blues captain Curtis Davies.
Nathan Redmond and Marlon King might have put Birmingham ahead before that, but Chris Hughton's side were forced onto the back foot in the second half, with former Liverpool youngster Ince to the fore.
Stephen Dobbie should have doubled the advantage following a sublime piece of skill from the 20-year-old winger before the Bloomfield Road faithful had hearts in mouths when King clipped the outside of the post in stoppage time.
Birmingham head into Wednesday's second leg at St Andrew's - their 62nd game of a season punctuated by runs in the Europa League and FA Cup - needing to bounce back from a first defeat in 10 outings, while Blackpool are now unbeaten in eight.
Ian Holloway reverted to the same Blackpool XI that beat Burnley 4-0 to secure a top-six berth a fortnight ago, with former Blues midfielder Barry Ferguson restored as captain in one of five changes.
Striker King came into the match on the back of scoring in both league games against Blackpool and the 18-goal forward returned as Hughton made four alterations to the side that beat champions Reading last weekend.
Gary Taylor-Fletcher prodded home from an offside position for the hosts, while Davies headed off target at the other end in a frenetic opening.
There was an early injury scare for Hughton when goalkeeper Colin Doyle hurt his shoulder colliding with the post as he collected Ian Evatt's header.
In the 13th minute, King fired an ambitious overhead kick past the post and moments later Redmond thrashed beyond the bar after Chris Burke found joy down the Blackpool left.
Evatt glanced wide as Blues full-back David Murphy botched a routine clearance from a corner, but by the time Seasiders midfielder Angel Martinez saw a spectacular volley dip over in the 25th minute the game's earlier intensity had quelled.
King might have done better when his shot from Burke's cutback clipped the top of the bar at the end of a clinical 40th-minute counter attack.
It was a miss he lived to regret a minute before the interval when Ince's 25-yard effort deflected off Davies and squirmed home past a wrong-footed Doyle.
Following a cagey start to the second period, Blackpool emerged as the stronger side and Blues full-back Peter Ramage produced a last-ditch block to deny Taylor-Fletcher from Matt Phillips' low cross.
In the 63rd minute, Ince collected full-back Neal Eardley's hopeful ball forward to dazzle the Birmingham defence with some languid twists and turns which deserved better than Dobbie's wasteful shot over from his subsequent pass.
Ince had established himself as the game's outstanding player and, having earned his side a free-kick in a dangerous position moments earlier, he danced in from the left and forced Doyle out to claw the ball from his toes.
Holloway introduced Nouha Dicko and and Kevin Phillips in a straight swap for forwards Dobbie and Taylor-Fletcher and the latter thought he had made an instant impact against his former club, only to be flagged offside after heading home a right-wing cross from namesake Matt.
King was agonisingly close to levelling the tie in the first minute of stoppage time, stretching to steer Wade Elliott's knockdown against the woodwork.