The Wales international, who came through the Cardiff academy and is the youngest player to have represented the Bluebirds, headed home the opener from a Mesut Ozil cross in the 29th minute.
Substitute Mathieu Flaimini doubled the lead with five minutes remaining before Ramsey completed the scoring in stoppage time to make it 15 goals for club and country this season and move Arsenal seven points clear at the top of the table.
Both Ramsey's goals were applauded by the two sets of supporters after another virtuoso display in what is turning into a stellar campaign and the player acknowledged the home fans by performing the club's 'Ayatollah' celebration after finding the net.
Wenger heaped praise on the 22-year-old and, when asked if £50million would be enough to prise Ramsey away from the Emirates Stadium, said: "No. We don't want to sell anybody, we want to keep the team together. I've suffered enough for years for having to sell the players.
"Now we are in a stronger position financially."
Wenger also believes Ramsey can get even better.
"He keeps surprising me," said the Gunners' boss. "He has matured as a player and a person as well. We came here in the FA Cup a few years ago and he had a very difficult game. Now he shows how much he has developed as a person.
"I was a midfielder and I would have loved to have what he has.
"He can defend, attack and score goals. What more do you want? He is also young - another quality that I have lost.
"He can still develop. When you see the improvement in him in the last two years then why should he stop now?
"There's more to come. If he continues to play like that then he will have a good future with Wales."
Wenger added: "The reaction of the fans was fantastic. I'd like to see that much more. I have a big respect for that. They are proud to be Welsh here."
Wenger and his team can now sit and watch nearest challengers Chelsea and Liverpool try to bring their lead back down to four points on Sunday.
The Frenchman remained coy about his side's title chances, but was delighted by their display.
He said: "I'm very pleased because we had a good performance. We scored three goals, but we were not only good offensively, we were also defensively sound.
"It was a mature performance and a focused one.
"We are showing consistency and that is always a good sign.
"I'm happy to have done the job here and to watch the other games tomorrow. All we can do is do our job and prepare for the next game."
Cardiff slipped to 17th in the table thanks to the defeat. The hosts were much improved after the break, with Wojciech Szczesny producing a great save to deny Fraizer Campbell an equaliser with the score at 1-0.
And manager Malky Mackay felt the final score was harsh on his team.
"The score is not a fair reflection of the game, but I am not going to apologise for having a go," he said.
"That's what we did, and we certainly gave them some problems in the second half. The calmness on the ball in the second half makes me very proud of the players.
"We were playing against a team who have had a manager in situ for 17 years. Over that time he has had a lot of money to build a recruitment process to bring in top players like we have seen here.
"We were playing against the best and were certainly not out of our league."
Mackay also has no doubt Arsenal have what it takes to retain their position at the top of the pile.
He said: "They've got a very good chance, if they are sitting first today.
"They are in the last-16 in Europe as well. It speaks for itself, it's not rocket science."