Stabilize the sections of undamaged ceiling around the opening with drywall screws placed a little back from the edge—this helps to avoid crumbling or buckling of your nice, clean-cut edge. Pic 1.

Use enough pressure when driving screws so that the screw heads imbed slightly into the wallboard surface.

Hold the screw gun at a slight angle and drive screws into the side rafters, starting the screws a little back from the edge as before. Pic 2.