Cardiff had looked set to earn a third successive win after goals from Michael Chopra and Roger Johnson had cancelled out Sylvan Ebanks-Blake's 21st of the season for Wolves.
But Konstantopoulos, who is on loan from Coventry, literally handed Wolves a point in the 81st minute.
He wasn't under any pressure but somehow managed to let a left-wing cross from Kyel Reid slip through his fingers and over the line. It was tough on Cardiff who had bounced back superbly after falling behind.
Faltering Wolves, who have now won just one of their last ten games, were grateful to take some reward from the game as the point extended their lead at the top of the table to four points.
But this was a match that they should have had wrapped up by half-time only to be let down by Andy Keogh's poor finishing.
Even before Ebanks-Blake struck, Keogh could have given Wolves the perfect start in the fifth minute only to see his close-range drive hit the post after Michael Kightly had dispossessed Michael Chopra.
Fortunately for Wolves, Ebanks-Blake proved to be more clinical and he made no mistake just six minutes later when he got away from the attentions of Gabor Gyepes to head home a Matt Jarvis cross at the far post.
Wolves should have rammed home that advantage by doubling their lead in the 21st minute but Keogh was guilty of a glaring, and costly, miss.
Ebanks-Blake saw his powerful drive spilled by Konstantopoulos and the loose ball flew straight to Keogh but the Irishman couldn't keep his shot down and saw his effort from six yards deflected over the bar.
It was a crucial error as Cardiff, who are now unbeaten in 12 league games, were back on level terms just ten minutes later.
Paul Parry was afforded far too much time and space on the right wing and he took full advantage to pick out Chopra who made no mistake with a clinical finish past Wayne Hennessey from 12 yards.
Parry's ability to deliver a telling cross proved crucial again just three minutes into the second half when Cardiff grabbed their second.
This time it was a corner from Parry that picked out the unmarked Johnson who stooped low to head past Hennessey from eight yards.
Johnson's goal looked to be the match winner only for Konstantopoulos to commit the error that cost Cardiff the chance to move into fourth place.