Writing surely is second
I'm going to have to go with the crowd here - surely writing supersedes the scientific method, and is certainly a precursor to both double-entry bookkeeping and the limited liability corporation.
If then we agree that the first two are agriculture and writing, the third would have to be something as world-changing as those two.
I think I'd still have to agree with what my high school history teachers taught - mass production (the assembly line), which sparked the industrial revolution. You could argue the internal combustion engine, but then you'd have to admit that fossil fuels were a precursor to that. You could also argue electricity generation, but again, without mass production, these inventions would not have made such a huge impact on history.
So there it is:
1. Agriculture (& animal husbandry)
2. Writing
3. Mass production
The relational database, the personal computer, semiconductors, or perhaps the internet would then be 4th. Just depends on which of those you think is more important.
Ok mass production maybe wouldn't have been possible without the limited liability corporation. But which of the two, if you had to choose one, had the greater impact? I think mass production, but you may disagree.