Emmanuel Adebayor grabbed a brace, with an own goal from Nicky Butt ensuring a comprehensive looking scoreline following what had been a decent first-half display by Kevin Keegan's men.
Eventually, though, the Gunners extra class showed.
"It was a game where the first goal had a big impact on the result," said Gunners boss Arsene Wenger. "We scored when we were in control and that was hard for Newcastle to absorb mentally.
"If they had scored in the first half, it would have given them more belief. We played against a good team who started well, but we eventually controlled the game in the second half. The second killed them. But overall, it was a difficult game."
Arsenal host Newcastle again in the Barclays Premier League on Tuesday night and manager Kevin Keegan believes there are some positives to take into the return to north London.
"It was a very good first half performance. We had the courage to play them," he said. "We were going along nicely and causing them problems, while they were not giving us much grief.
"We could not keep it up and they stepped up, we stepped back and in the end, the gulf was pretty big."
Keegan added: "Our biggest problem is confidence.
"When the first goal went in, you could not really see us coming back from that.
"At times, our passing in the second half was X-rated stuff, we were just giving the ball away.
"But if we can put 90 minutes in like we did in the first half, then Arsenal will have a tough game here - although you can still play well for 90 minutes against them and they can turn you over."
Keegan maintained captain Michael Owen is "looking really sharp", but admits the striker, who has not scored in the Premier League since October, needs goals.
He said: "Michael is nearly back to where he wants to be. If he had scored a goal today, you would have been saying what a good performance it was.
"He is looking really sharp, it us just goals now.
"We have not been creating much for him and if I had been standing up there up front, I know what I would have been saying to my manager at the time - 'I don't mind chasing stuff, but who is going to give me that bit of quality I want?'
"If we get him opportunities, he will score."