The former Sheffield Wednesday man is just past his 34th birthday but he showed more alertness in the box than players ten years his junior to score in the 14th and 66th minutes.
It was a game the Terriers dominated for most of the 90 minutes and on this showing their play-off ambitions may have some substance.
Cheltenham, meanwhile, look set for a long hard winter if they fail to compete in the manner they displayed in this one with manager Keith Downing admitting afterwards that his team were "second best in every department."
The opening goal arrived from virtually the first serious chance of the game when Robbie Williams' free-kick from wide on the right spun back to him off the defensive wall. Williams lifted the ball into the area and Booth was the only man moving through a static defence to volley his team in front.
Cheltenham showed little cohesion at all going forward until the start of the second half but Huddersfield blocked them out with central defenders Nathan Clarke and David Mirfin dominant.
The second goal settled the contest with Booth holding the ball up and laying it wide to Danny Schofield. His cross found the veteran striker in acres of space on the edge of the area and his looping header evaded Cheltenham goalkeeper Shane Higgs and sailed into the top right-hand corner of his net.
Dean Sinclair forced a good save from Huddersfield goalkeeper Matt Glennon and Ashley Vincent dragged a shot wide for the home side late in the game but by then the outcome had long been decided.