The Scot will replace Roger Federer in second in the world rankings if he wins the title in Miami this weekend and last night he saw off the challenge of Croatia's Marin Cilic 6-4, 6-3 to reach the semi-finals.
Murray eased into the last four without losing a set and his performance against Cilic, after a shaky start, was his best of the fortnight to date. "I thought it was a good match, from my side," Murray said. "I had that 0-40 in the first game and then lost serve but the good thing was that every time I was broken, I broke back immediately."
Murray, the clear favourite for the title following the surprise defeat of world No.1 Novak Djokovic in the fourth round, will tonight face the winner of last night's match between the Czech Tomas Berdych and Richard Gasquet of France.
It was only last September that Murray found himself a set and 5-1 down to Cilic in the quarter-finals of the US Open only to turn the match around. Five days later, he won his first grand slam title.
Yesterday, he recovered quickly from an early break down and once he hit his stride, his baseline game was a notch above where it had been in the early rounds. A brilliant backhand pass set up a break for 5-4 in the first set and Murray served out comfortably before racing ahead 5-2 in the second set.
With defeat approaching, Cilic, the world No.11, began to cut loose and it paid off as he got one of the two breaks back but Murray then broke in the following game, even though he needed seven match points to get the job done.
There is significance to becoming world No.2, since it would guarantee that Murray would be in the opposite half of the draw to Djokovic in the grand slams.
There is, of course, the small matter of Federer and Rafael Nadal and where they were to fall in the draws. However, as Murray's coach, Ivan Lendl, pointed out this week, when Nadal falls to No.5 – as he will do on Monday – then Murray could have the luck of the draw and find Djokovic, Federer and Nadal all in the opposite half. Equally, he could draw Nadal in a quarter-final.
"I'm just thinking about the matches," Murray said, when asked if becoming No.2 is now in the forefront of his mind. "My goal this week was always to get as many matches as possible; if I do that, the rankings will take care of themselves."
It is the standard answer but a sensible attitude in a tournament that has already delivered more than its fair share of surprises, a number of them provided by Tommy Haas, a veteran German whose best days had seemed to be long behind him.
After five operations in an injury-hit career, Haas enjoyed a superb 2012 and has worked his way back inside the top 20 at the grand old age of 34. His victory over Djokovic was a huge surprise but he followed it up with a thrashing of the Frenchman Gilles Simon and today he will play David Ferrer, the No.3 seed, for a place in the final.