Roberts, a £250,000 close season signing from Ipswich, showed his class with the coolest of finishes to kill off this Carling Cup tie just past the hour.
Roberts, a menace on the right wing, also hit Town's fourth nine minutes from time as Huddersfield destroyed their League Two opponents.
Former Huddersfield skipper Jon Worthington, fighting for his future under new boss Stan Ternent, headed the opener three minutes after the break.
Left-back Robbie Williams claimed the third with a superbly-struck free-kick.
In a goalless first half, Roberts went close when he forced Rhys Evans into a tip-over save after good work from Danny Cadamarteri.
Roberts thought the goal was about to open up for him just after that but defender Graeme Lee produced a well-timed saving tackle.
City should have scored through new signing Michael Boulding, who was making his first start after his move from Mansfield.
Barry Conlon headed on a free-kick which keeper Matt Glennon failed to hold and Boulding spurned the chance after slamming it into the side-netting.
Midfielder Worthington popped up in the box just after half-time when Cadamarteri laid off for Williams to set up the opener which Worthington dived in to score.
Roberts' solo effort came in the 63rd minute when he collected a loose ball in midfield, ran forward and drew Evans before slotting home.
Williams, whose place at Town is also under threat after the arrival of David Unsworth, smashed home a 25-yard free-kick to end the contest.
Roberts made it 4-0 thanks to the persistence of Cadamarteri who almost scored himself.
Cadamarteri saw Roberts was better placed and the winger had a simple finish from close range.