The Olympic champion overcame torrential rain and gale force winds to secure his fifth grand slam final place.
US Open: Andy Murray defies elements and Tomas Berdych to reach final
However, he will have to wait until Monday to take on either David Ferrer or Novak Djokovich after the men's final was put back a day as conditions deteriorated.
The weather in New York was decidedly Scottish, with the match delayed by torrential rain and then played in the teeth of a howling gale, which Murray coped with better than his opponent to win 5-7 6-2 6-1 7-6 (9/7).
And the 25-year-old was explaining his feelings at one of the stranger victories of his career when two gatecrashers entered his press conference.
Security was not needed, though, as it turned out Sir Sean Connery and Sir Alex Ferguson had popped in to congratulate Scotland's biggest sporting star.
It was the first time Murray had met either of the men and he posed for pictures as Ferguson joked: "We've been telling everyone how Scotland invented the world. Today we invented the wind."
When the press conference resumed, Murray said: "It's great. It's obviously nice to have their support. Hopefully they'll be back for the final as well."
It quickly became clear the match would be decided by which player managed better in the wind, and the feeling was - with Murray's tactical and varied game - it would suit him better than the big-hitting Berdych.
That was not the case in the first set, though. Murray broke first for 2-1 but was then broken straight back after being forced to replay a point when his hat blew off.
Both players were finding it particularly tough serving into the wind and Murray came unstuck when he served to stay in the set in the 12th game, Berdych breaking with a powerful forehand winner.
The Czech had played remarkably well and it was Murray getting frustrated but a break at the start of the second set changed the momentum and he won 14 of the next 17 games.
The Scot looked completely in control at 3-0 up in the fourth set and with break points to make it six games in a row but Berdych held on and then rediscovered some of his early form to break back.
He forced a fourth-set tie-break and took advantage of the wind to lead 4-1, but Murray levelled at 5-5 and then saved a set point with some brave attacking play.
Berdych saved the first match point with an ace but two forehand errors gave the victory to his opponent, who will play in a second consecutive grand slam final after losing to Roger Federer at Wimbledon.
Describing the conditions, which frequently caused play to be stopped while rubbish or even chairs blew across the court, Murray said: "It's probably the toughest I have played in.
"It was pretty much four hours, and it was brutal. There were a few games in the fourth set where it calmed down a little bit, but it was very, very tough conditions to play in."
Berdych admitted Murray had coped better than he had, with the Czech making 64 unforced errors compared to 20 for his opponent.
It was a major disappointment for the sixth seed, who held a 4-2 head-to-head record over Murray before the match and had played one of the best matches of his career to beat Federer in the quarter-finals.
He argued there should be the option of postponing such a big match in those conditions, saying: "It's something which should be at least thought about.
"We are here in the States where they really love a show. But this is not about a show. This is just about somehow trying to deal with the conditions and then trying to put the ball over the net. Sometimes it was impossible, but that's how it is.
"He dealt with that much better than I did. The wind blew it away from me."
The weather has played havoc with the tournament in the last few years and the women's final, which had been scheduled for Saturday night, was postponed well in advance because of the poor forecast.
The second semi-final between Novak Djokovic and David Ferrer began and the Spaniard had taken a surprise 5-2 lead when play was abandoned for the day to enable everyone in Flushing Meadows to travel home before an expected tornado hit.
Murray felt the conditions were playable, saying: "I don't know if they stop in other sports for a lot of wind. When there is a tornado around then that's pretty serious. I think that's the right time to stop.
"There is a skill to playing in the wind. I have never played in it when it's been that bad but people like to watch professionals struggle when they're in tough conditions.
"[Coach] Ivan [Lendl] always says he likes watching the golfers when it's blowing really hard, because it makes them hit bad shots and makes people feel a lot better [about their own game]."
Murray is certainly in the best position as he will now have a day off before the fifth Monday final in as many years, while Djokovic and Ferrer have to finish their semi-final on Sunday.
The boot was on the other foot for the Scot four years ago, when he beat Rafael Nadal on the Sunday before playing Federer in his first grand slam final, losing in four sets.
He added: "I didn't get the day off then and maybe it hurt me a little bit. Novak and David are very, very experienced so I'm sure they will deal with the situation better than I did back then anyway.
"But it will be nice to get a rest tomorrow and also to be able to practise and get your rhythm back. Because some of the shots I was playing out there today I certainly won't be playing if it calms down."