Cristiano Ronaldo settled a scrappy Group I affair in Faro by bundling the ball over the line at the second attempt in the 72nd minute.
It was Ronaldo's 23rd goal in European Championship qualifying and finals, taking him one clear of the previous record held by Denmark's Jon Dahl Tomasson and Hakan Sukur of Turkey.
Until the breakthrough, Portugal had toiled against their stubborn opponents, but Quaresma, on as a replacement for Danny, brought a save out of Armenia goalkeeper Roman Berezovski, allowing Nani to force the rebound into the path of Ronaldo, who did the rest.
Quaresma had also come off the bench to supply the winning goal for Ronaldo in the 1-0 victory over Denmark last time out, and Santos was delighted with another telling contribution from the Porto man.
"Quaresma a secret weapon? No, he's no secret weapon," he told RTP.
"At that time we felt that we needed a man to create and pass, so we decided to gamble on Quaresma and the truth is that he did very well.
"I was expecting it not to be easy. I had seen the games of this team [Armenia] against Serbia and Denmark. They defend a lot and then have two or three very quick players up front.
"I think we had a very good initial 15 minutes and if we had scored then the game would have become simpler.
"We tried to play in the opponents' area and try and win the rebounds. Often these games are won in rebounds. I think the victory is entirely fair.
"What is the significance of the record of Cristiano Ronaldo? It has a great significance for him, for the team, for the country, and of course for me as the manager."
