© PA Photos
The visiting Foxes dominated for large periods of the match but were frustrated by stubborn Blues defending and their own wasteful finishing.
It was Martyn Waghorn who was guilty of missing Leicester's best chance of the opening period, blazing the ball over from inside the six-yard box after he was found unmarked by King's cross.
It was a similar story after the interval, as Butland produced two world-class saves to deny Waghorn and Danny Drinkwater equalising goals.
However, Marshall eventually broke the Birmingham resistance with almost the final kick of the match, evading two Blues challenges before shooting in off the post from 25 yards.
There was nearly time for Leicester to find a winning goal, but Birmingham hung on despite having Jonathan Spector sent off in the dying stages.