Exeter, who rested a number of players with Monday’s Johnstone’s Paint Trophy area final looming, dominated the first half but could not get the goal their play deserved.
The Terriers opened the scoring after 55 minutes when a long ball forward was not dealt with by the Exeter defence and Danny Cadamarteri rolled the ball under Artur Krysiak and into the net.
Cadamarteri then provided the assist for the second goal 12 minutes later, setting up Gary Roberts who fired home with his right foot from 12 yards out.
A shocking error by Krysiak led to a soft third for the promotion-chasing Terriers, with Anthony Pilkington on hand to slot home from close range 10 minutes from time.
Exeter’s misery was complete when Kevin Kilbane rattled in a fine shot from 25 yards two minutes from time before Daniel Nardiello netted a stoppage-time consolation from six yards out.