Shelvey's deflected shot put Newcastle ahead and his second, from 25 metres, put the visitors 3-0 up after Ayoze Perez had scored with a left-footed strike.
Further goals followed after the break from Ciaran Clark, Aleksandar Mitrovic and Grant Hanley.
Newcastle, relegated last season, have 15 points from their opening seven games, one behind Huddersfield.
"We now have to show we can concentrate in every game. It doesn't matter if we score six goals, we get three points in the end and now have to concentrate on the next game and not lose that concentration," manager Rafa Benitez said.
Newcastle lost their opening two games of the season but have won five in a row since, conceding only one goal.
(Reporting by Martyn Herman; Editing by Clare Fallon)
