Steven Lawless hit a double early in the second half after Kris Doolan had opened the scoring for Thistle and, despite Graham Carey grabbing a consolation goal for County with a deflected shot, there was no way back for the Highlanders.
The result continued a good start to the season for Partick, who drew their league opener against Motherwell last week, and Archibald is happy to have points on the board.
He said: "We were desperate to get a good start and we've kicked on from last season.
"The overall team performance was excellent - we worked hard in training this week on what we were going to do and what we were going to play."
Thistle even had the comfort of leaving some of their new signings out with the bulk of the team being the same as the one that played in the First Division last term.
Archibald added: "The team out there was more or less the team that won the league last year. They have done well at the start of the season but the new guys will get the chance. It will be a long season we'll get injuries and dips in form."
County boss Derek Adams admitted his side's performance was the worst display since he took over.
He said: "It was probably the worst performance since I became Ross County manager. We didn't perform well enough, collectively it was a very poor performance."
But the 38-year-old was quick to praise Premiership newcomers Thistle who have won all three of their competitive matches this season.
He added: "Partick played well, they closed us down and were very energetic and forced us into mistakes.
"In possession we weren't good enough. Next week we will have to change things about.
"We didn't create enough in the game. The defence play was very poor and offensively we didn't cause Partick much trouble until late in the first half.
"I watched them against Dundee United last Friday night and they played ever so well. So it is no surprise how well they have done. But from my point of view it was poor."