Booth tapped home the only goal of the game on the hour mark after Michael Collins’ toe-poke was parried by Rovers goalkeeper Danny Coyne.
Tranmere went closest to breaking the deadlock in a lacklustre first half through Chris Shuker with 31 minutes gone.
The winger raced onto Chris Greenacre’s deft pass, only to be foiled by Huddersfield stopper Matt Glennon, who produced a fine save.
Booth almost grabbed his second late on but was unable to convert a goal-line scramble, with Coyne snuffing out the opportunity as Tranmere offered little.
Town substitute Danny Schofield could have put the result beyond doubt when he was fed by Andy Holdsworth on 78 minutes, but he was thwarted by Coyne.