Newly-appointed captain Kenny Miller opened the scoring from Charlie Adam’s corner after 18 minutes before Wigan’s James McArthur doubled Scotland’s lead with a sublime lob.
Celtic winger Kris Commons then completed a sweeping move shortly after the break to seal a victory which puts Scotland level on points with hosts Ireland.
“We played very well.” said Levein afterwards. “I have been talking constantly about players at their clubs playing a very high standard and how much improvement there has been in a lot of players in the last year.
“But it is one thing me talking about it. It is important the players take that onto the pitch and prove I am not talking a lot of rubbish.”
He added: “The fact we played as a team was the most pleasing thing.”
The Scotland manager was particularly impressed with his side’s work ethic. He continued: “Every player on the pitch worked their socks off to help each other.
“That for me is invaluable. We can have good individual performances – people scoring goals, keepers making saves – but the actual willingness to do the hard work, the work without the ball, was the most pleasing part of the game.
“I have been watching them play week in, week out for their clubs and tonight was about producing a performance that was reminiscent of a good club performance.
“To that end I got everything I wished for.”
Scotland’s next international clash is against Wales on 25 May ahead of a meeting with tournament favourites Ireland four days later.
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