The Seasiders could even afford the dismissal of substitute Claus Jorgensen, who lasted less than 20 minutes before seeing red following an off-the-ball altercation with Lee Bowyer.
McLeish's men on the other hand have now won just one in seven and look to have plenty to do to seal an automatic return to the Premier League.
Ex-Blues forward DJ Campbell headed the Seasiders in front after just 13 minutes for his second goal in two games on loan from League One Leicester City.
Dead-ball specialist Ian Harte almost doubled the home side's lead on the half-hour but saw his free-kick fly just wide.
However the lead was extended after 37 minutes with a stunning strike from 25 yards by midfielder Keith Southern, his second goal of the season.
Alx McLeish's men were looking distinctly below par although Bowyer almost cut the deficit just before the break, but his goalbound effort bounced off Blues forward Cameron Jerome.
The visitors introduced James McFadden for the second half and the Scotland international went close within just five minutes, but saw his long-range effort curl just wide.
The introduction of Kevin Phillips breathed new life into the visitors' challenge and had Sebastian Larsson won a free-kick and Jerome with a shot from inside the box, found the target the comeback may have been possible.
However, Parkes' men remained well organised and might even have made it three, but Roy O'Donovan, on loan from Sunderland, saw his snap shot turned round the near post by Maik Taylor.