Rhodes struck after 44, 50 and 52 minutes and has now scored 11 goals this season for a Terriers side who returned to their early-season form.
Lee Novak slammed Town in front with a crisp curling shot in the 17th minute after Michael Collins had squared Antony Kay’s throughball into his path.
More goals for Town seemed likely as Peter Clarke and Rhodes both hit the crossbar in the first half, while Kay’s persistence forced City goalkeeper Oscar Jansson to brilliantly tip his effort over.
Rhodes made it 2-0 with a near-post header from a Robbie Williams cross, while Anthony Pilkington and Gary Roberts supplied the crosses for the ex-Ipswich forward to complete his hat-trick.
Exeter had early chances through Stuart Fleetwood and James Dunne, but were rarely in the match once Town took the lead. City’s former Town striker Marcus Stewart was given a standing ovation by the fans when he was substituted after 63 minutes.