The Scots-born world No 3 was twice pegged back by Federer before sealing a punishing five-set victory to set up a clash with world No 1 Novak Djokovic in tomorrow's final.
Murray beat Djokovic to win the US Open last September but is aware he will have to be at his best again to overcome the 25-year-old Serbian star who is a three-time Australian champion.
But speaking after a gruelling four-hour struggle against Federer in Melbourne, the Dunblane star, twice a losing Australian finalist, said he believes he is better prepared.
"When you lose the fourth set having served for it, maybe 18 months ago I wouldn't have come back from that so I think mentally I've probably become stronger because of the results at the end of last year," he said.
"I don't think loads has changed in my game, I just think I am understanding what I need to do in the important moments.
"I've been questioned for large parts of my career about physically would I be strong enough; mentally would I be strong enough; do I listen to my coaches, blah, blah, blah, blah, blah, whatever it is, can I handle pressure?
"I think those years of having all of those questions and then finally to be able to answer them, I think, yeah, it was all part of the process.
"So I hope on Sunday I can play a good match. Obviously, having won against Novak before in a Slam final will help mentally."
Celebrities in the crowd included former Australian cricketer Shane Warne, who showed he's lost none of his talent by catching a wayward shot with one hand.
For Murray, beating Federer in Melbourne was a world away from the tears he shed on Wimbledon's centre court when he was beaten by the Swiss in the final. "I'm getting closer," he said then, as he broke down.
Yesterday, the pride of Scotland punched through the last of his frustrations with both fists.
First Minister Alex Salmond said the whole country would be behind Murray tomorrow, while Prime Minister David Cameron tweeted: "Congratulations Andy Murray on reaching yet another Grand Slam final. Best of luck – we will all be cheering you on."
Experts say Murray and Djokovic are arguably now the dominant pair in the game.
David Marshall, chief executive of Tennis Scotland, said: "On form they are probably numbers one and two in the world right now. Hopefully if Andy does win on Sunday the No 1 ranking could be a reality in the months to come. That is a target he's set, but it depends what happens in the French Open and Wimbledon."