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Stephens's 57th-minute goal proved sufficient in downing the Blues, who struggled in their attempts to finish the opportunities they forged throughout the encounter.
Both sides struggled to create chances throughout an insipid opening to the game, with neither goalkeeper finding himself heavily involved in proceedings.
Birmingham striker Nikola Zigic thought he had scored the game's opening goal midway through the first half, only for it to be chalked off, with the Serbia international adjudged to have fouled goalkeeper Ben Hamer in the build-up.
As the half grew older it was the visitors who looked most likely to break the deadlock, with defender Dan Burn nicking the ball away from striker Simon Church at the vital moment in front of goal, before Johnnie Jackson thumped a shot narrowly wide.
Charlton boss Chris Powell has defender Michael Morrison to thank for preserving the lead, as the 25-year-old twice cleared off the line; first from Zigic, before repeating the feat to deny Tom Adeyemi.
Second-half substitute Peter Lovenkrands spurned arguably the opportunity of the game in the dying embers, as the former Newcastle United forward blazed over from 10 yards following Zigic's knock-down.