Ok, I can't take the credit for myself, because I adapted Two On Two Off's tutorial on attaching a skirt facing by machine. And many sewers probably already do this.
After attaching the invisible zipper, I turned the dress inside out so that the dress and linings' right sides were together. The zipper is on the inside, underneath the lining.
Using a regular zipper foot, I stitched down the center back seam to the end of the zipper. You can't sew too close to the zipper underneath or it will be difficult to zip it up when turned right side out.
Here is the inside with the dress turned right side out:
Yay, no hand-stitching!