His form earned a call-up to Cotter's first Scotland team, which travelled to Houston and beat USA 24-6 on Saturday evening.
Glasgow full-back Stuart Hogg and fit-again Edinburgh wing Tim Visser dotted down for the hosts but Russell stood out for Cotter.
"Finn Russell, you'd think he's played 20 or 30 games already," said the head coach. "He was composed, he kicked well out of his hand, he directed play well and defended.
"Obviously I'm happy because we got the win. I thought the players, despite the difficult conditions, played well.
"With certain things, as all coaches will say, we have to do better next week and we're working on those.
"I'm really pleased with the opportunities created and I'm happy that we managed to get over the line. I thought we could've got over and scored another couple. We're looking at that but the opportunities were created and that means that we had initiative."
Ulster's Andrew Trimble continued his excellent international form, crossing over as Ireland completed a 29-17 win over Argentina in Resistencia.
It was the winger's fifth try in seven international appearances and there was also room on the scoresheet for Ulster teammate Chris Henry, while Leinster's Ian Madigan added a pair of penalties.
Another Ulsterman was in action as South Africa triumphed against a World XV - scrum-half Ruan Pienaar pulling the strings for the hosts.