Rhodes drilled in his 21st of the season on 38 minutes after Tommy Miller pounced on a slip by a Carlisle defender and put the Scotland ace in the clear.
The hitman missed a great chance to win it in the last minute when put through by Scott Arfield. He shot wide having already gone past goalkeeper Adam Collin.
United, seeking a sixth away win of the season, took the lead after just eight minutes. Keeper Ian Bennett's misplaced clearance was knocked to Carlisle's Francois Zoko by Town's Oscar Gobern while Antony Kay rashly dived in but failed to stop Zoko.
It proved costly as Zoko pulled the ball back from the byline towards the penalty spot and Liam Noble rushed in unmarked to crash home a low drive.
Huddersfield went closest to a winner after the break when Lee Novak's deft close-range flick from a Danny Cadamarteri cross was tipped onto the post by keeper Collin.