Beckett, who hit six goals in warm-up matches to the new campaign, grabbed the only goal to give the home side a winning start.
Former Oldham striker Beckett was often the odd man out under Peter Jackson last term, but with Andy Ritchie now at the helm Beckett has a fresh start.
Beckett headed the only goal from Danny Schofield's cross in the 17th minute and that was the highlight of a less-than-inspiring contest.
The Terriers, beaten twice by Yeovil last season, were always on top and it was only when they tired late on that the visitors threatened.
Ritchie was forced to alter his line-up when new signing Danny Cadamarteri pulled up with a hamstring strain in training on Friday. With Andy Booth also struggling with a similar problem, Ritchie paired Beckett with winger Schofield.
Beckett and Schofield didn't have much support from midfield, but gave the Yeovil defence plenty to think about with an energetic display.
Malvin Kamara blasted well wide and Schofield's skidding cross only just eluded Chris Brandon at the far post.
On the stroke of half-time Schofield's powerful goal-bound drive hit Terrell Forbes painfully in the groin.
Chances were few in the second period and, as Huddersfield started to run out of steam, the Glovers had two opportunities to snatch a point.
Nine minutes from time new recruit Lloyd Owusu was one of three Yeovil players left free in the box, but he stumbled and his weak shot was gathered by Matt Glennon with the goal at his mercy.
New-look Yeovil still need time to gel and Lee Peltier, on loan from Liverpool, should have done better with a header straight at Glennon.