Aitor Karanka's side showed excellent character to rescue a point from a precarious position at St Andrew's, Patrick Bamford scoring the equaliser 16 minutes from time.
Middlesbrough goalkeeper Dimitrios Konstantopoulos was the man sent off after bringing down Clayton Donaldson in the 43rd minute.
Substitute keeper Tomas Mejias could not keep out the resultant penalty, scored by Paul Caddis, as Birmingham headed to the break on a high just one day after the club's owners went into receivership.
But Chelsea loanee Bamford ensured the travelling fans went home happy after slotting past Darren Randolph following a one-two with Grant Leadbitter.
In Wednesday's other match, Bradford City continued their play-off push with a 2-0 win at struggling Leyton Orient in League One.
James Hanson scored a first-half double for Bradford, who have beaten Chelsea and Sunderland en route to the FA Cup quarter-finals.
Bradford will play Championship outfit Reading in the last eight on March 7.
