Rhodes, a £150,000 summer buy from Ipswich, drilled a loose ball into the net from 20 yards just before half-time to put Huddersfield 1-0 ahead.
The 19-year-old then made a sensational start to the second half by scoring again and having another goal ruled out in the space of only a few seconds.
From the restart, he headed home an Anthony Pilkington cross, which was flicked on by Lee Novak only for the effort to be ruled offside.
Stockport took the resulting free-kick, but Rhodes pounced on the misplaced clearance to put Town two goals up with a 20-yard curler - his third goal in just two games for the club.
And Huddersfield sealed victory 15 minutes from time with a blistering Theo Robinson solo effort, although County substitute Adam Griffin grabbed a late consolation by firing low into the bottom-right corner through a crowd of players.