Rhodes wasted a free header in the opening stages before putting Town ahead after 12 minutes. Gary Roberts crossed from the left and the Terriers' top-scorer headed in off the underside of the crossbar with the aid of a deflection.
Rhodes doubled his side's advantage soon afterwards, heading another Roberts cross into the top left-hand corner at the near post.
Wednesday hit back though and drew level with two goals in three minutes. Skipper Rob Jones headed in the first in the 26th minute after good work by Ben Marshall before left-back Reda Johnson slotted home to equalise.
On-loan winger Marshall slid the ball past Huddersfield goalkeeper Ian Bennett to put the Owls ahead just after the hour mark and Chris O'Grady headed in Chris Lines' free-kick to make it 4-2 with 74 minutes on the clock.
Rhodes fired in right-footer to complete his hat-trick with 13 minutes remaining before poking home an equaliser in the seventh minute of added time to cap a sensational Yorkshire derby.