Australia international Nick Carle was shown a straight red card for a two-footed lunge on Blues striker Cameron Jerome in the 75th minute - but Alex McLeish's side failed to breach Palace's resolute back line as the Championship high-fliers missed the chance to move to within a point of leaders Wolves.
Palace started much the brighter, with teenager Victor Moses, in particular, causing problems for the Midlanders.
However, Blues slowly edged their way back into the game and Jose Fonte had to clear off the line from Seb Larsson before Marcus Bent's rasping drive flew just wide in the 14th minute.
And it was Bent who missed the best chance of the opening 45 minutes, sending his thumping header inches wide of the post from Larsson's pinpoint cross in the 27th minute.
Alan Lee should have made the Midlanders pay for their wastefulness - but his poor cut-back after Maik Taylor's scuffed kick was easily cut out with Moses, John Oster and Neil Danns all waiting to slot into an empty net.
Danns had a strong penalty appeal turned down by referee Mr Taylor on the stroke of half-time much to the disbelief of Palace boss Neil Warnock.
The Blues missed two glorious chances in the opening stages of the second period, first through Lee Bowyer who shot wide with just Julian Speroni to beat in the 48th minute and then Honduran Carlos Costly stroked wide in a one-on-one duel with Palace's Argentine shot-stopper.
As both sides struggled to find any rhythm, Blues were handed a numerical advantage after Carle's sending off despite the midfielder's protests that he played the ball.
Jerome missed another guilt edged opportunity for Blues in stoppage time and the south Londoners held on for a point.