Roberts, an early substitute for the injured Danny Ward, smashed in an angled volley from around 12 yards after 24 minutes after Jack Hunt's free-kick was only half-cleared by Ian Goodison.
Rovers goalkeeper Owain Fon Williams, playing in a fluorescent orange kit, was one of the few other highlights of a scrappy affair in which neither side really got going. He and a defender combined after 28 minutes to clear a goalbound Jamie McCombe header from off the line.
Fon Williams then tipped over a Alan Lee header just before half-time and turned a Jordan Rhodes effort round the post at the start of the second half.
At the other end, Tranmere had a goal ruled out after 60 minutes from the game's best move. Former Huddersfield player Lucas Akins, Robbie Weir and Enoch Showunmi were all involved, with Max Power being marginally offside when he crashed a 20-yard belter into the roof of the net.
Huddersfield, now unbeaten in 32 league games, sealed victory after 82 minutes when substitute Arfield stroked home from the edge of the box.
