DUNWOODY, Ga.—United Parcel Service Inc. and rival FedEx Corp. have already made themselves as indispensable to Christmas as Santa Claus.

This season, though, they're taking a much more active role in holiday shopping than just delivering packages for retailers like Amazon.com Inc., Apple Inc. and Nordstrom Inc. UPS and FedEx are racing around neighborhoods trying to lock in consumers with door-to-door, even door-to-office customized deliveries that make them more concierge than delivery service.

UPS...