There's a Better Way: Large Drywall Patch
When making a large drywall patch, all you need is a scrap of plywood and some drywall screws.
William Barstow of Arcata California writes:
Here is still another way to install a drywall patch in a spot that doesn’t have any backing. First, cut an oversize patch, and nibble away at it until it fits the hole. Next, find a piece of plywood or lath that is longer but narrower than the hole. Slip the wood behind the drywall, and position it so that it spans the hole, as shown in the drawing. Drive drywall screws through the wallboard and into the lath to draw it up tight to the back of the gypboard. Screw the patch to the lath, and you’re ready to fill the cracks with joint compound.