You can do this with an experimental version of the jpegtran utility with the "drop" option. Get it from http://jpegclub.org/jpegtran/. Here's an example (using a sample image from http://www.rawsamples.ch/). I've uploaded all samples here as PNG files to avoid any extra recompression from the hosting service.

First, the image in high quality JPEG:

This is 1715K — over a megabyte.

Now, dropped to terrible-quality (10% in Gimp, with 4:2:0 subsampling):

Whooo, down to 52K. JPEG is amazing.

So, next, I tried the suggestion from StephenG; I took the low-quality version and put it on top of the uncompressed original, then erased the section I want to look best — the trumpet-vine cloth in the top row. That yields:

But, unfortunately, this is now back up to 667K, which kind of defeats the purpose. Even when I go to 4:2:0 subsampling, it's still 378K — and this is a more fair comparison, as you'll see in a bit.

So, I tried the jpegtran -drop approach — I cut out an overlay of the part I want high quality:

which is 38K, by the way, and used

jpegtran -drop +592+62 overlay.jpg -outfile dropped.jpg lowq.jpg

to paste it in. I discovered that the subsampling has to match, so I couldn't use the ultimate high quality, but that's probably okay.

for a final 221K image. This is a significantly better size result than resaving as high-quality, even with subsampling. However, it's arguably a worse visual result, as you can't blend — it needs to be in straight lines, and everything snaps to 8×8 chunks. You could get around this by carefully doing the edge chunks individually, with intermediate levels of compression so the transition isn't obvious, but that seems... tedious.

So, if you need one file, you could do this. And, if the square crop and block alignment issue works with your image, it might even be the best way.

However, since you're presenting on a web page, I'd take a different approach: use CSS, and put your high-quality area in a PNG file with transparency, and put that right on top of the low-quality JPEG. And in your case, where the high-quality area is small (0.5% of the image!), it's probably the best.

Of course, this only works if your high-quality area is small enough for that to be a compression win. If it's large enough, you're back to trying some of the above.