The Terriers came out on top at the Galpharm Stadium in Saturday's battle of last season's defeated League One play-off semi-finalists.
Rhodes was put in by a ball over the top from Gary Roberts on 39 minutes and he planted a stunning 25-yard lob over Ross Worner as the Addicks keeper came rushing out.
The former Ipswich forward was also involved in Town's second goal just two minutes later when Worner brought him down in the box.
Rhodes again ran onto a through ball and the home players were livid when referee Graham Salisbury ruled Worner got the ball first. But from the resulting corner, swung over by Graham Carey, Jamie McCombe leapt to head in at the near post.
The result was put beyond doubt when on-loan Celtic winger Carey, who caught the eye with his attacking runs, crossed for Roberts to smash in a lovely half-volley eight minutes from time.
It took until stoppage time for Charlton to finally get a shot on target. Substitute Matt Fry evaded some attempted tackles and let fly from 20 yards, with the shot finding the net with the help of a deflection.