Cardiff had looked set to pick up a sixth win in the last seven games before central defender Johnson sliced a Zoltan Gera cross into his own net in the 88th minute.
It was rough on Cardiff who had twice been two goals in front, but a just reward for battling Albion.
Quickfire Paul Parry took just 27 seconds to put Cardiff in control and doubled their advantage in the 33rd minute with his sixth goal of the season.
Substitute Roman Bednar's tenth goal in 12 games gave Albion hope before Joe Lesley's second-half strike looked to have made the game safe.
But Martin Albrechtsen set up a rousing finale when he reduced the arrears in the 71st minute before Glenn Loovens handed Albion a hard earned point.
Albion were caught cold straight from the kick-off when Parry collected a pass from Gavin Rae waltzed through their backline and lifted the ball over Dean Kiely from 20 yards.
Unsurprisingly, it took Albion some time to get to grips with that setback and it wasn't until the 25th minute when they first really threatened.
It needed a fingertip save from Michael Oakes to keep out a 35-yard drive from Kevin Phillips.
When Bednar saw his shot deflected wide two minutes later, Albion appeared to be getting on top.
But their revival came to a shuddering halt in the 33rd minute when Parry raced on to a clearance by Darcy Blake and cut in from the right wing and raced past Albrechtsen before firing an angled drive beyond Kiely,
This time, Albion's response was immediate. Captain Jonathan Greening lifted a free-kick into the area and Bednar was on hand to steer his close-range header beyond Oakes.
But their hopes of a comeback were dashed seven minutes into the second half when another surging run down the wing proved to be their undoing.
Ledley made and scored the goal when he left right-back Carl Hoefkens in his wake.
There was a stroke of luck about the strike as Ledley's misplaced cross flew straight back to him but the Wales international made no mistake with a low left-foot drive from 12 yards.
To their credit, Albion did not buckle and they were rewarded for their persistence 19 minutes from time when Albrechtsen struck.
Phillips saw his header saved by Oakes, but the ball was crossed back in by Brunt to Albrechtsen who made no mistake with a header from eight yards.
Albion then laid siege to the Cardiff goal and there pressure was finally rewarded through the unlucky Johnson.