The world number four was rarely troubled by the challenge of Kei Nishikori, winning in straight sets in the early hours of Wednesday as he maintained smooth progress through the draw in Melbourne to reach the semi-finals.
Britain's big hope, who recently linked up with new coach Ivan Lendl, will face Novak Djokovic in the last four on Friday as he bids to land a first grand slam title and a third straight Australian Open final appearance.
Judy Murray has just returned from Australia, where as captain she had also been scouting the AEGON GB Fed Cup team members ahead of the BNP Paribas Euro/Africa Zone Group 1 competition in Eilat, Israel from February 1 to 4.
She feels everything is going as well as can be expected for her son.
"I was in Australia until Sunday - but did not get up at 3:30am today," she said.
"I am not always there, I went to all of the slams last year, but that was the first time I had done all four of them because Andy did not have a coach.
"This year he has a coach and his girlfriend with him, and I have my job to do.
"I just woke up and found he had won, with no stress."
On the potential in her son's link-up with Lendl, who claimed eight grand slam singles titles but was unable to secure a Wimbledon crown, Judy Murray said: "It is still a little bit early to tell. He only started with Ivan a few weeks ago in their relationship, but all I can say is 'so far so good'."
Britain will jet out to Israel on Thursday with a group headed by the long-serving Anne Keothavong and Elena Baltacha, who travel along with youngsters Heather Watson and Laura Robson.
"We have a great team, a very balanced team with experience and youth," said Murray, who was appointed to her Lawn Tennis Association role in December with the aim of taking Britain up into World Group II when they clash against Holland, Portugal and hosts Israel next month.
"We have a reasonably favourable draw, have been analysing our opponents and that will be very important for us to decide the match ups for our team.
"I came into it at fairly short notice, so I have been to as many tournaments as I can to see everybody.
"I have enjoyed getting to know the girls and it is an exciting time for women's tennis in Britain.
"We have some good young players coming up behind as well, so for me it is going to be a big challenge, but an exciting one."
GB will need to top their group and then win a play-off in Eilat if they are to qualify for April's World Group II play-offs.