Rhodes, who has now scored 13 goals in his last five matches, put Town in front in the fourth minute when North End goalkeeper Iain Turner fluffed an attempted clearance, leaving the Scotland Under-21 international with an easy tap-in.
The striker then crashed in his second off the post in the 42nd minute with a fine header from Jack Hunt's curling cross and the third was created by Scott Arfield's 57th-minute through-ball, with Rhodes showing great composure to turn past the last defender and fire low into the bottom-right corner.
It means Rhodes has scored back-to-back hat-tricks in the league following his three-goal blast at Exeter last week. He also scored a hat-trick for the Scotland Under-21s against Luxembourg, meaning he hit trebles in three of his last five games for club and country.
Preston, who slumped to a fourth straight defeat, played their part in an entertaining contest. Town goalkeeper Ian Bennett brilliantly saved Iain Hume's deflected goal-bound shot, while Terrier skipper Peter Clarke denied Adam Barton with a goal-line clearance.
The visitors scored a consolation in the 61st minute when Hume's low cross was turned in at the far post by Juvhel Tsoumou.