If the threads of the cap were facing up–which they were–I could have simply inserted the bottle into the threads, screw it on by turning the bottle, and pull. However, since the cap was further down the drain than the bottle’s mouth would reach, I had to find another solution.
Fortunately, I thought to use a screwdriver with a screw.
Preferably use a magnet tip screwdriver so you don’t drop the screw. In this case, the sink was only full of sudsy water, so no toxic, harmful, or nasty floaties to worry about. Your situation may vary. This solution should also work if the plug is from a bottle cap with threads facing down, a rubber ball, or other object that can be easily penetrated with a screw.
Simply, push the screw into the cap or object, and turn clockwise.
Be careful not to damage it too much as you turn the screw in, or you may not be able to pull it later. A side benefit of puncturing the bottle cap was that the water began to drain.
Once you have the screw inserted a good depth into the cap or object–leaving sufficient length of the screw to grab onto–pull the plugged object out with your hand.
In cases where the object may be really stuck, you may try using pliers to grip the screw instead of your hand.
Congratulations, you just saved the day! Now go check off that item in the “honey-do” list.