A cup tool for use with a high-pressure mandrel of a wellhead isolation tool has a three-part packoff assembly that slides over a cup tool tube from an unset position to a set position. The three-part packoff assembly includes an elastomeric cup, a rigid alignment ring located above the elastomeric cup and an elastomeric packoff element located above the rigid alignment ring. The rigid alignment ring helps ensure that the elastomeric cup remains correctly aligned in a casing or tubing that is not straight, is out of round or is washed, and helps ensure that the elastomeric packoff achieves a high-pressure seal in the set position, even under adverse downhole conditions.