In a way there was no such single discovery.
Initially it wasn't even clear what an element is. By definition, element was a "simple" substance - one that can not decomposed further. However, some substances were treated as elements, as early chemists/alchemists were not able to decompose them into simpler substances. Some of these substances were later found to be compounds.
Number of elements was for long time unknown and slowly growing, around the time Mendeleev published his periodic table it became obvious that elements properties follow some pattern, but even at the time it wasn't clear how many are there. However, PT put a limit on the number of simple substances - assuming they had to follow the pattern, there was only a limited number of places in PT. This approach was once proven to be partially false, with the discovery of noble gases.