Master Yi's Q+W can negate a large portion of Zed's burst damage, even going as far as to completely negate Zed's ult if your timing is good.
Furthermore, Master Yi wins any DPS based slap fight with Zed thanks to Double-Strike and Wuju Style's passive. So long as you keep even, you can win most trades.
And finally, if Zed chooses not to fight at all due to Master Yi's burst negating and Master Yi's usually superior DPS, Master Yi's whole 'I'm the strongest of the melee carries and your anuses will remember this' schtick that all Master Yi's are known for will eventually mean that Master Yi out scales Zed even if they are even on farm.
Just so long as you know how to abuse Q's invincibility and W's damage resistance, Master Yi can outpace Zed in almost every scenario.
Just to prove that I do have experience with this.