The main point of epiphany in the Cask of Amontillado is when Montresor first starts to wall Fortunato into the recess at the end of his vaults. There are two different successes that this epiphany is important to: one is the success of the endeavor of Montressor, and the other is Poe's success in building the suspense in this story.
Montresor needs the sudden epiphany, otherwise his whole plan would be ruined. If Fortunato were to slowly figure out what was going on (or even worse if he was told from the beginning), he could fight back, he would be more likely to resist Montresor when Montresor was trying to kill him. The sudden realization of Fortunato that there was no pipe of Amontillado, that Montresor's whole story had been a farce, created a sense of shock in him that allowed Montresor the time to chain Fortunato to the wall and start to rebuild the wall, effectively trapping him in.
It is important to the success of the story because of the suspense. Half the fun of this story for the readers is trying to figure out what Montresor plans to do for his revenge. Is he going to poison Fortunato with the Amontillado? Is he just going to scare his unwitting victim? So many options allow the readers to let their imaginations run free, trying to figure out all the creative things that Poe could have intended. When the reader suddenly learns what Montresor intends, it is quite the surprise. Trapping Fortunato in a recess in the catacombs is something that the reader never would have suspected, so the reader also gets the surprise that Fortunato felt.