Seven minutes into the second half, Blues' comeback was complete when Cochrane atoned for his earlier lapse as he curled over a cross from the left and Stansfield found space at the far post to guide home a header past the leaden-footed Okonkwo.
A further seven minutes later, Blues were two goals clear when Paik Seung-ho fed Japanese midfielder Iwata, who fired home a low, swerving shot from 25 yards which found the bottom right corner.
It could have been more - but instead things heated up close to the centre circle when tempers flared after a coming-together between Cochrane and Wrexham substitute Paul Mullin.
That sparked a large brawl involving all 20 outfield players, clearly enjoyed by the watching Brady.
James McClean was to the fore, earning one of the five bookings dished out by referee Scott Oldham, which also included Bielik, Blues sub Keshi Anderson and Wrexham subs Mullin and Andy Cannon.
When Blues skipper Bielik then went in late on Cannon, he was sent off for a second yellow card.
But the damage was already done to well beaten Wrexham by a Blues side who go second, level with their opponents and also third-placed Charlton Athletic, all on 13 points.