The Terriers were in complete control once Paterson scored his first goal for the club in the 11th minute and could have scored more before Clayton drilled home a game-clinching second after the break, with Connor Wickham converting a late consolation for the Owls.
Paterson and Clayton appear to have put their alleged recent training ground bust-up behind them.
The pair were left out of the matchday squad for last month's home win over Leeds following reports of a training ground altercation, and boss Robins saw the funny side when they celebrated Paterson's opener with mock fisticuffs.
"It's fitting that they got on the scoresheet together," said a smiling Robins.
"I do things a certain way, but by no stretch of the imagination can we afford to leave our better players out for long periods, but they've got to tow the line.
"I'm pleased for them, but I'm pleased for everybody, I thought we were outstanding."
Robins added: "Paterson is a top player. It's taken him a little bit of time to settle down for whatever reason, but if he performs like that he will be a handful in the Championship."