Albion, who had lost their last three games, looked to be heading for a priceless win when Paul McShane fired them ahead in the 64th minute.
When Birmingham were reduced to 10 men just two minutes later after Julian Gray was sent off for hauling down McShane, Albion appeared set to cruise to victory.
But Johnson came up with a wonder strike in the 86th minute that was all the sweeter following the events when the teams last met in October.
Johnson suffered a broken jaw that day in a clash with Albion left-back Paul Robinson.
But he had the last laugh this time when he latched on to a header from Cameron Jerome to fire home an unstoppable volley from 20 yards.
It had all looked so different when McShane swept in his third goal of the season by converting a Jason Koumas cross that looked to have put Albion's promotion firmly back on track.
But Johnson's late leveller leaves them still in sixth place and with a massive battle on their hands to try and secure a top-two finish.
Birmingham could easily have taken all three points had their £2.5million striker Rowan Vine not wasted two golden chances.
He had already blazed wide in the 22nd minute from close range after being picked out by Martin Taylor's header before being presented with an even better chance on the hour.
Vine only had Dean Kiely to beat when he met Johnson's right-wing cross but his shot was superbly beaten away by the Albion goalkeeper.
Albion had held the edge in terms of chances created in a low-key first half but failed to really test the Birmingham goalkeeper Colin Doyle.
Nathan Ellington twice went close before Birmingham were lucky to escape on the half-hour when Diomansy Kamara was hauled down by Stephen Kelly and from the resulting free-kick Koumas curled his shot inches wide.
Kamara then blazed over the bar three minutes later after a mazy run down the wing.