A multi-needle quilting machine (20) is provided with a tape or ribbon guide (30) that is operated by a method by which a narrow strip (32) is fed against a facing layer of a wide multi-layered material (24) as it is fed into the quilting machine. In the quilting machine, series of chain stitches are sewn, at least one of which joins the tape (32) and layers of the multi-layered material (24) together with the same thread in a quilting process, thereby applying the tape (32) to the quilted product in a single quilting operation without the need for a post-quilting tape application step. The tape may form a decorative strip or have unsewn sections that serve as handles for a mattress when the quilted product is formed into a mattress cover. The quilting machine, the tape application attachment, the quilting method, the quilted panels, and mattresses having the quilted panels are claimed.