A strike from Tom Ince on the stroke of half-time came off the centre-back's leg and left goalkeeper Colin Doyle helpless to prevent the only goal of a game littered with offside flags and midfield battles.
Ince had earlier been denied a goal by the assistant referee, as were substitute Kevin Phillips and Blues striker Marlon King in the second-half.
King sent a gilt-edged chance wide at the death from Jordan Mutch's deft volleyed lay-off and Chris Hughton's side must now win on home turf in Wednesday's second leg in order to stand a chance of reaching the final at Wembley.
The home side went on the attack almost immediately from kick-off, and had the ball in the Birmingham net on five minutes courtesy of Ince, only for the winger to be offside as he collected Stephen Dobbie’s deflected effort.
The visitors would bounce back to enjoy their own spell of possession, coming close to opening the scoring after half an hour when Chris Burke’s cross was headed back across goal by Wade Elliott, only for Nathan Redmond to fire over from decent range.
But it was Blackpool who had the lion’s share of opportunities in a mostly cautious first half, with Angel Martinez sending a leaping volley over on 32 minutes before Dobbie’s wicked drive forced a great parry from Doyle on 38.
And with one minute remaining of first half regulation time, Ince’s effort from outside the box found its way into the Birmingham goal courtesy of the ankle of an unwitting Davies.
The Seasiders continued to have the bulk of the enterprising play as the second half rolled around, and only a superb block from Peter Ramage prevented Gary Taylor-Fletcher from burying Matt Phillips’ low cross from the left just shy of the hour mark.
The Blues back line were caught napping three minutes later, allowing Ince to collect the ball and slip it through to Dobbie, only for the striker to lean back for his placed finish and watch it head over the intended top corner.
Ian Holloway threw on a second Phillips in the form of the veteran striker, and his headed finish from a floated cross with 13 minutes remaining appeared to put the home side comfortable until the flag reared its ugly head for the umpteenth time.
And despite their superiority over 90 minutes, Blackpool were lucky not to head to St Andrew’s on even keel when an early ball from the left-hand side at the opposite end of the pitch was put on a plate for King by Mutch, only for the forward to miss the target with an opportunity he should have buried.
The second leg will be played on Wednesday evening, kick-off at 19:45.