You pretty much answered your own question. If you want to really make it harder for users to cheat, send game log to the server, where you'll calculate the score.
You don't have to send all the events, just ones that affect result score.
There are some techniques, though, that may help you:
include signature in your request. Something like MD5(secret_key + params). Although, "secret key" will have to be in JS source, it will effectively protect you from simple request interception (see Tamper Data and Charles)
if it's a multiplayer game, accept scores calculated by clients and compare them. Cheaters will be pretty visible (assuming that the majority of users are honest).
you can set a score cap, an "unreachable" result. Everyone who posts score higher than this is a cheater. For example, speed typing game: no one can type correct text at 1500 chars/minute, even 700 is pretty damn hard (though achievable).
