The Terriers were given a helping hand with some shocking defending from the Grecians. Goalkeeper Artur Krysiak endured a torrid time and was substituted at half-time.
Alan Lee opened the scoring in the eighth minute when he beat the hapless Pole to Scott Arfield's cross and Rhodes, who also netted a treble against the Grecians two years ago, made it 2-0 when he capitalised on a mix-up between Krysiak and Danny Coles.
Exeter rallied after the break and had a Daniel Nardiello goal disallowed, while Guillem Bauza headed straight at Town goalkeeper Ian Bennett, but Rhodes made it 3-0 when he rifled in a volley from six yards.
Lenny Pidgeley, who replaced Krysiak, then flapped at Town winger Danny Ward's cross to allow Rhodes to head in from close range to complete his hat-trick and an all too easy win for the Yorkshire side.