A brace from the impressive Caolan Lavery, a goal from Leon Best and an own goal from Will Packwood left City reeling, and they headed home with a solitary Lee Novak goal as consolation.
Stuart Gray's side gladly returned to winning ways in South Yorkshire after successive defeats to Yeovil and Wigan in the last week.
They were given a helping hand by Lee Clark's side, though, who continue to leak goals at will, with Wednesday grateful beneficiaries.
Birmingham have gone four without a win now and, although they are eight points clear of the drop zone, will do well to brace themselves for a nervous run-in as their form evades them.
It was all one-way traffic early on as Sam Hutchinson fired in an effort that went just over and Atdhe Nuhui's teasing cross could not be turned in.
Chris Maguire then forced Darren Randolph into a smart save with a free-kick before the pressure told as Lavery ran on to a Kieran Lee cross before placing a strike beyond the keeper with 17 minutes gone.
City had no time to take in what had happened either as Best doubled the lead three minutes later, tapping in after Maguire flicked on a Lee corner.
Birmingham's response this time was good and had Novak been quicker he would have made good an opportunity to race clear one-on-one.
It would have been three at the break had Nuhiu's effort not been disallowed for an infringement by the towering striker.
He rippled the side-netting with another hit after the break too, before Packwood showed him how to finish, albeit in his own goal, as he turned a Jeremy Helan cross beyond Randolph just before the hour.
Birmingham's best efforts were long-range ones from Emyr Huws and their bluntness in attack was highlighted further as Lavery added his second in the 68th minute, curling in from the edge of the box after clever tee-up play from the impressive Maguire.
After that Wednesday eased off, knowing full well the points were safe, and Birmingham duly got on the scoresheet.
With nine minutes left a Chris Burke delivery found Novak who, with no need to run past anyone this time, prodded in, but it was nothing more than a token effort.