Scotland seemed set for victory when Darren Fletcher struck with eight minutes to go but Kadlek blasted his spot kick into the roof of the net after Danny Wilson was harshly adjudged to have tripped substitute Jan Rezek in the 90th minute.
World champions Spain are commanding leaders in Group I with maximum points from five games while the Czechs remain in second on 10 points from six matches. Scotland move up to third on five points from five games.
Only one runner-up from the nine qualifying groups will qualify automatically and the best the Czechs can probably hope for is second place behind Spain and a play-off slot.
They played with plenty of invention and should have taken the lead in the opening minutes when Milan Baros wasted a gift-wrapped chance, firing over the crossbar after he had been teed up by Petr Jiracek.
Scotland took the lead against the run of play just before half-time when Fletcher played in Kenny Miller whose shot evaded the attempted save of keeper Jan Lastuvka.
NEAT FOOTBALL
For all the Czechs's neat football after the break they needed a rather unorthodox equaliser when Jaroslav Plasil turned the ball into the net off his stomach from a cross after 78 minutes.
In a tense finale Scotland went back in front when Miller seized on a defensive slip to race towards goal. He then teed up skipper Fletcher with a perfect diagonal pass and the Manchester United midfielder calmly rolled the ball into the opposite corner of the net.
The celebratory mood of the fans soon turned sour though and they were further incensed when Scotland had a penalty claim turned down when Christophe Berra tumbled in the area and was booked for diving by Dutch referee Kevin Blom.
"I've got to be careful what I say. What I can say is that we lost the game not through anything we did wrong," Scotland manager Craig Levein told BBC radio.
"I lay the blame on the referee's shoulders. Two huge mistakes. Berra gets brought down and is booked for diving!".
Spain will qualify for the finals if they beat Liechtenstein on Tuesday while Scotland must beat Lithuania the same day to keep their slim hopes alive.
'I think that’s the respectful thing for two captains to do after a game. I probably boiled over a bit at the end, with a bit of everything coming out': Jarrod Bowen lifts lid on heated clash with Mario Lemina after West Ham's win over Wolves
Arsenal want Dan Ashworth - for a VERY different kind of revolution
