Put on safety goggles. Brace your ceiling with a T-brace made of 2-by-4 lumber. Set the brace on a piece of plywood under the sagging seam. Press on the lowest-hanging section of ceiling with the brace until the panels are pushed back against the ceiling joist.
Scrape away the tape and loose pieces from the seam, using a putty knife. Thread wallboard screws through wide, thin washers. Drive the screws between the seam and into the joist every four inches to secure the panels to the joist.
Take down the T-brace. Remove any debris from around the seam and washers with a putty knife.
Spread joint compound over the seam, screws and washers until the seam is filled. Apply a strip of fiberglass mesh tape, then cover with jointing compound for wide seams. Smooth the compound over the area with the putty knife. Allow the compound to dry.
Sand the repair with fine grit sandpaper. Prime, then paint if desired.