Midfielder Arter struck the only goal in the 19th minute to inflict back-to-back defeats on the record-breaking Terriers.
Town's history-making 43-match unbeaten run was ended two weeks ago by Charlton and this defeat was a first at home since Boxing Day last year.
Wesley Thomas set up the winner when he collected a ball down the right channel, beating Calum Woods. As debutant Alex Bruce, on loan from Leeds, came across to cover, Thomas kept his cool to pick out the unmarked Arter who fired home from the centre of the box.
Marc Pugh's brilliant reverse pass then set up Simon Francis but his shot crashed into the side netting and Town keeper Ian Bennett produced a superb tip-over to deny Scott Malone.
Town's misery was compounded as right-back Jack Hunt was carried off with a suspected fractured ankle.