The solution is to never lift off the gas.
If you're lucky, it's just a bad U-joint. Check the pinion nut to make sure it's tight. If it just loosened up, you may have caught it in time that the gearset isn't damaged. Just be sure to stake it this time, or replace it with a new one. Getting the torque right on these is the trick. But it also could be loose because one of the bearings went bad.
Less likely is that the rear end is moving more than it used to because a U-bolt is loose, center pin snapped or leaf broken.