Substitute Thievy Bifouma looked to have snatched all three points late on for West Brom, who led 2-0 after just 10 minutes, before Mats Daehli - who also came off the bench - levelled at the death to salvage a precious point and drag West Brom further into the mire.
Morgan Amalfitano and Graham Dorrans had eased any nerves around The Hawthorns early on as Pepe Mel's side looked on course to give their fans a rare performance to cheer.
However, Jordon Mutch and Steven Caulker found the net in an impressive comeback for the visitors, who then showed character to deny Albion again in a breathtaking finale.
Mel had described the game as a "final" in the build-up and his side were certainly up for the big occasion, as Amalfitano put West Brom ahead with a lob from an audacious angle early on.
With moments of genuine quality lacking in the hosts' season to date, the Marseille loanee conjured up a delightful effort to break the deadlock with the West Brom faithful on their feet again soon after when Dorrans doubled the lead.
Amalfitano was again involved as his lofted delivery found its way to the Scot, who slid the ball home to put his side in control.
Mutch - scorer of two goals in Cardiff's 6-3 defeat to Liverpool last weekend - was on target again to reduce the deficit as his lofted effort caught out Ben Foster.
Only Mutch will know if he truly meant to go for goal, but a back-pedalling Foster was beaten as Cardiff were handed a lifeline before the interval.
Captain Caulker looked to have got the crucial goal 17 minutes from time but the late drama continued in a game neither side could afford to lose.
Thievy scored what looked to be the winner, but Daehli earned the visitors a potentially vital point that keeps their survival hopes alive while Mel will be left to rue West Brom's inability to capitalise on their strong start.
Mel's side made an ideal start when Amalfitano produced a lob of the highest quality to take David Marshall completely by surprise after just two minutes.
His effort came from a nigh-on impossible angle outside the area, but the Frenchman lifted the pressure around The Hawthorns with arguably one of the goals of West Brom's season.
Cardiff's visit to the West Midlands got worse just seven minutes later when Dorrans burst into the area and finished Matej Vydra's knockdown.
It capped off a nightmare opening 10 minutes for Cardiff, who were not allowed to settle by their rampant hosts.
Fraizer Campbell almost got on the end of Andrew Taylor's delivery from the left as a shell-shocked Cardiff gradually grew into the game, without showing enough of the attacking threat that saw them twice lead title hopefuls Liverpool last week.
Despite looking toothless for large periods before the break, Foster mirrored his opposite number in being caught out by a looped effort just after the half-hour mark.
The end of the half played out with relatively few chances before Mel was left frustrated by missed chances from Youssouf Mulumbu, Vydra and James Morrison.
The visitors too failed to muster too many opportunities of note until Caulker angled a looping header over Foster.
In dramatic fashion, West Brom thought Thievy had secured them the three points before Daehli struck to cap off an exhilarating affair at the foot of the table.
