Lee Novak's low cross from the by-line was turned in by Scotland international Rhodes, who has scored five times in his last two games, at the near post in the 34th minute.
Rhodes, now on 20 goals for the season, had been denied four minutes earlier by a brilliant last-ditch clearance from Chesterfield striker Drew Talbot, who hacked the ball off the goalline.
Rhodes, a menace in the first half, should have put the Terriers in front in the 12th minute, but fired straight at visiting goalkeeper Tommy Lee from Alex Bruce's pass.
Chesterfield, who have not won in 13 league matches, came more into it after the break and nearly levelled when Dean Morgan fired just wide in the 66th minute.
Spireites striker Jordan Bower also narrowly missed the target four minutes later, but Huddersfield clung on despite some desperate defending towards the end.