Town had much the better of the early exchanges and it needed a good save by Gunnar Nielsen to deny Alan Lee after eight minutes.
But the keeper could do nothing about a fine lobbed effort from the edge of the box by Rhodes in the 18th minute after a long clearance had been helped on by Lee.
As Tranmere rallied, Lucas Akins bungled a free header from a Scott Wootton centre while an angled shot by John Welsh was comfortably held by keeper Alex Smithies.
Tranmere missed a great chance to level matters after 56 minutes. A penalty was awarded after a challenge by Gary Roberts on Ash Taylor but the spot-kick by Lateef Elford-Alliyu was saved by Smithies diving to his left.
Nielsen made solid stops from Scott Arfield and Rhodes as Huddersfield increased the tempo after the hour mark. The visitors eventually doubled their lead after 67 minutes with Rhodes again the marksman as he turned in a cross by Lee following a swift counter-attack.