The Oxford English Dictionary's earliest citation for "seed" as a sporting verb comes from an American article published in 1898 (the noun follows later), but it seems likely that this is a relatively recent inclusion because as late as 1924 the Times felt it necessary to explain to its readers exactly what the term meant - and the writer sniffily advances the fact that the usage is not in the OED as evidence of "how little seeding accords with British notions". There is no explicit etymology for the phrase but the image is presumably straightforward - every seed packet carries detailed instructions about the optimum distance to be left between seeds to ensure the best results and the graphic representation of a tournament's early rounds even looks a little like the furrows of a ploughed field. Though "seeding" also has a chemical meaning - when you "seed" a solution you introduce small particles to start off a process of crystallisation - this seems far less likely as an origin than its horticultural sense. For the Times, the idea that you would carefully plant your best prospects into a competition, spacing them out to ensure plenty of room to grow, was clearly not quite fair play. For the Americans, it was simply common sense - elementary husbandry which ensured an even and abundant harvest of vigorous late rounds. There are no guarantees, though, whether you're growing corn or exciting tennis games.
From time to time the weeds defeat the seeds, or, as St Matthew, a tennis correspondent before his time, put it: "And some fell among thorns; and the thorns sprang up and choked them."