Striker Paterson and midfielder Clayton were left out of Huddersfield's matchday squad for last month's home win against Leeds amid reports the pair had been involved in an altercation during training the day before.
Northern Ireland international Paterson, a summer signing from Burnley, has since been out of action due to a hand injury, but returned to the side to score his first goal for Huddersfield when he gave them an 11th-minute lead.
Clayton, back in the starting line-up following a four-game absence, fired home Huddersfield's game-clinching second in the 68th minute as the visitors secured their second away win of the season in the Championship.
Connor Wickham netted a stoppage-time free-kick, but it was another testing afternoon for the Wednesday faithful, who have seen their side win just once in the league this season, while a sixth league defeat has heaped more pressure on under-fire manager Dave Jones, whose side remain in the bottom three.
Huddersfield boss Mark Robins made six changes to the side beaten at home by Birmingham in their last match and was rewarded in the 11th minute when Paterson opened the scoring.
Clayton dissected Wednesday's defence with a clever pass into the penalty area and although James Vaughan was clearly offside, Paterson was deemed by the linesman to be level and he steered a fine finish beyond on-loan Arsenal goalkeeper Damian Martinez.
Wednesday did not muster their first shot on goal until the 29th minute when Jose Semedo sliced an effort on the edge of the area wide.
Martinez, making his first appearance for Wednesday, was forced into a low save from Oliver Norwood's dipping long-range drive shortly before the break and although he was not troubled further, opposite number Alex Smithies had by far the easier first half as the home side were booed off at the interval.
The visitors should have doubled their lead inside the first minute after the restart, but with the goal at his mercy after Paul Dixon's low shot had spun off a defender, the unmarked Vaughan side-footed against the outside of Martinez's left-hand post.
Wednesday's half-time substitute Jermaine Johnson, who replaced Michail Antonio, blazed high and wide when well-placed just inside the area.
At the other end Paterson also scuffed his chance of his second goal following Dixon's cross.
Jermaine Johnson went close to an equaliser in the 56th minute, but his left-footed curler was brilliantly saved by Smithies, who was not so impressive soon after when opting to punch away Wickham's speculative effort.
Huddersfield struck a deserved second in the 68th minute when Norwood's 25-yard shot rebounded back to Clayton and the former Leeds midfielder fired low into the bottom corner from 12 yards.
Wednesday looked more potent going forward following the introduction of Jermaine Johnson and the Jamaica international saw another goalbound effort, a low right-footed shot, superbly saved at full stretch by Smithies.
Wickham's low free-kick was saved by Smithies and he was on target with another effort in stoppage time, but that consolation did little to stifle further boos from home fans at the final whistle.