The Lowland League champions were the better side but Cowdenbeath missed a late spot-kick when Kyle Miller’s effort was saved by Matthew McGinley.
Cowden manager Gary Locke said: “It was a really tough game. In hindsight not getting beat and being at home next week is not the worst but we had the best chance of the game.”
Cowdenbeath’s Fraser Mullen sent in a fierce drive after only 23 seconds from 25 yards but home goalkeeper McGinley was alert enough to block.
The hosts’ first chance came on 14 minutes when Craig McLeish sent a 25-yard dive flashing just wide and shortly afterwards Joao Victoria set up Sean Winter who fired over at the second attempt.
The deadlock looked all set to be broken eight minutes from the break when Winter’s flick was only partially stopped by Jamie Sneddon but Miller popped up to clear.
East Kilbride screamed for a penalty on 64 minutes when Adam Strachan went down however he was booked for his trouble with the hosts’ frustration growing nine minutes later when Victoria rattled the woodwork.
The game looked to be petering out until the late penalty drama with K-Park boss Martin Lachlan saying: “It is a game that we could have won as we had good chances. I was surprised at their penalty as it was the only time the assistant got involved.”