The midfielder, recalled to Lee Clark's starting XI, pounced to convert in the 71st minute after Paddy Kenny could only parry Nathan Redmond's long-range effort - with the clash appearing destined for stalemate.
The lively Ravel Morrison had fired against the crossbar in an opening period dominated by the home side, with Ross McCormack's free-kick into the penalty area clipping the woodwork for the visitors at the start of a second half which they edged.
The victory - only Birmingham's third in 12 league games at St Andrew's - takes the Midlands club up to 10th in the npower Championship table and finally secures their second-tier status amid what is an extraordinarily congested battle to avoid the drop.
Leeds, also mathematically safe, drop into the bottom half having won both of their fixtures since the appointment of McDermott earlier this month - with the former Reading boss unable to conjure up an away win for a United side who have tasted success just three times in 22 attempts on the road this term.
Morrison, on loan from West Ham, was pulling the strings in the opening exchanges and almost broke the deadlock with a superb curling effort which came back off the crossbar, and midway through the first half, Jack Butland produced a wonderful save to tip over Michael Tonge's 20-yard strike.
Redmond, like Morrison, was enjoying a lively afternoon and he fired straight at Kenny as the clash continued to flow, with Mullins then failing to find the target from eight yards when he really should have done better.
McCormack's free-kick into the penalty area clipped the top of the crossbar at the start of the second half as Leeds immediately set out to pose a greater threat than they had in the opening 45 minutes, but it was Birmingham who broke the deadlock.
Redmond, anonymous in the second period, cut inside and fired a shot from distance which was only parried by Kenny straight into the path of Mullins, who converted the rebound from six yards.
Rudy Austin forced a great save from Butland from distance soon after but Leeds failed to launch an assault for an equaliser and it was Birmingham who posed the greater threat in the latter stages as they went in search of a second.