I don't have any evidence to back this up, but I think the influence is probably a lot less direct. My guess is, most turn-based JRPGs do not get their game mechanics from DnD, but get them from other turn-based JRPGs (such as Final Fantasy and Dragon Quest).

Now I have heard that DnD did have a big influence on Final Fantasy, which makes sense. So I guess we could say they get their game mechanics from DnD indirectly. But I am not entirely sure to what extent DnD influenced Final Fantasy. Obviously there was some influence, but how much exactly? (I can see it in other parts of the game's design as well. Apart from the game mechanics, there is the class system which must have come from DnD. But it's also worth noting that another influence was the early Studio Ghibli films: the chocobos were borrowed from Nausicaa and the airship was borrowed from Castle in the Sky.) I would also think that text-based adventure games were another influence. And less directly, Tolkien was probably an influence (but not for the game mechanics).

I have not played a lot of DnD, but I will point out that it's not very similar to any of the JRPGs that I've ever played. DnD is probably closer to a WRPG (but, then again, I haven't played a whole lot of WRPGs either).