The Railwaymen should have opened the scoring after a goalmouth scramble saw Pope hit the crossbar and Michael O'Connor had a shot well blocked before Moore fired over.
Crewe keeper John Ruddy kept out Lukas Jutkiewicz at the other end before Pope crashed another shot against the Terriers' woodwork.
The visitors took the lead in the 30th minute when Jutkiewicz picked out James Berrett for an easy finish from 12 yards, but their lead lasted just two minutes as Moore lashed a stunning 20-yard volley past Alex Smithies.
Ruddy pulled off a wonder save to tip over Gary Roberts crashing header on the stroke of half-time, but Crewe took control with two quickfire goals after the break.
In the 59th minute Pope robbed Andy Butler by the corner flag before driving into the box and unleashing an unstoppable left-foot shot around Smithies and two minutes later, Donaldson made it 3-0 with an acrobatic overhead kick.