Lilian Nalis headed wide, David Norris missed distance and Maik Taylor saved from Akos Buzsaky as Plymouth attacked.
Neil Danns missed from 12 yards for Blues before Pilgrims' Barry Hayles forced Taylor into action again.
Taylor made a superb save from Buzsaky after the break and Hayles headed wide from close range before Jaidi headed home Gary McSheffrey's corner.
Birmingham manager Steve Bruce:
"You have to stand up and be counted and we stood up to be counted and a little bit of quality in the end has won us the game.
"But overall Plymouth can feel that they have been harshly done by that they have not got something out of the game.
"Of course you need a little bit of luck but then ability comes into it and Maik [Taylor] was exceptional."
Plymouth: McCormick, Connolly, Seip, Aljofree, Capaldi, Norris, Nalis (Summerfield 88), Wotton, Buzsaky (Djordjic 76), Hayles, Chadwick (Ebanks-Blake 62).
Subs Not Used: Larrieu, Sawyer.
Birmingham: Maik Taylor, Kelly, Jaidi, Martin Taylor, Sadler, Danns (Larsson 58), Muamba, Clemence (Nafti 88), McSheffrey, Jerome (Gray 69), Bendtner.
Subs Not Used: Doyle, Campbell.
Booked: Muamba, Jerome, Clemence.
Goals: Jaidi 75.
Att: 17,008.
Ref: G Hegley (Hertfordshire).