>Iori (having essentially powergrinded his skills from fighting on the front lines in a grail war) understands Musashi because he literally trained under him
>They have a 1 on 1 fight
>Musashi leaves an opening that Iori is prepared to exploit
>Musashi didn't know that Iori learned Tsubame Gaeshi so she isn't prepared to deal with it
>Iori nails her with it while she's completely unable to guard
>She loses
Knowing your opponent is portrayed as the key to victory multiple times in the story. It's (part of) why Iori even does his goody-two shoes "act", so he can understand the people around him.
This is the same reason why Saber beats Iori too, which is what the flashbacks in the cutscene after were meant to portray. Add Fate's sword magic autism and being closer to mystery and it makes sense that Iori could keep up with Musashi (Who was also under a worse class, being a Berserker)