A storm delayed the start of play and, although the rain cleared, an extremely strong wind blew the whole way through the match, disrupting play on numerous occasions and making life extremely tough for both players.
But, although Murray lost a tight first set, it was he who coped with the conditions better, surviving a fightback in the fourth set from Berdych to win 5-7 6-2 6-1 7-6 (9/7) in three hours and 58 minutes.
It will be the 25-year-old's second consecutive grand slam final after his Wimbledon loss to Roger Federer and his second US Open final, with his first experience of a major showpiece coming here in 2008, when he also lost to Federer.
Talking about the conditions afterwards to CBS, Murray said: "You have to focus for every point. The chairs were flying onto the court, it was hard to serve.
"It's some of the hardest conditions I've ever played in and I come from Scotland so that's saying something."
He added: "From the end of the first set I was in control. At 3-0 in the fourth I had three break points, but from the far side of the court it was very tough so I got broken in the next game. I just tried to hang in there and I did a good job at the end."
The result also means Murray will overtake Rafael Nadal to become the new world number three, but most importantly it gives him the chance to claim his first grand slam title.
Murray will meet either defending champion Novak Djokovic or Spain's David Ferrer in the final and, asked if he feels this is his time after winning Olympic gold, Murray said: "I hope so.
"You can never say for sure, I know how hard these tournaments are to win. David and Novak are top, top players.
"When the conditions are like this, anything could have happened. I'll give everything in the final."
Murray went into the match as the favourite by ranking and experience at the latter stages of grand slams but also knowing Berdych had won four of their six previous matches.
The big-hitting Czech had also served notice of what a threat he would be by blasting past Federer in the quarter-finals.
The wind was certainly the winner in the early stages as the stands slowly filled up and planes roared overhead.
Murray piled the pressure on Berdych in a lengthy third game and got the break when the sixth seed drilled a forehand just wide.
Murray thought he had saved a break point in the next game but Berdych protested he had been distracted by his opponent's hat blowing off and, after a heated exchange between the two men and umpire Pascal Maria, the point was replayed and the Czech broke back to 2-2.
Berdych was struggling with his ball toss to such an extent that at times he was serving at little more than 80mph but he was certainly hitting the ball cleanly off the ground.
Holding serve into the wind was the main problem and Murray was furious with himself that he did not put more pressure on his opponent in the 11th game.
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That left him serving to stay in the set for a second time and he could not manage it, the Scot struggling to keep his cool as Berdych broke through with a mighty swipe of his forehand.
Murray was clearly fired up and immediately had three break points at the start of the second set, taking the second when Berdych pushed a forehand long.
The Scot seemed to be enjoying himself a bit more now, taking on the challenge instead of being frustrated by it, and he broke again to lead 4-1.
Berdych held to force the third seed to serve out the set, but no sooner had Murray thrown the ball up for his first serve than a gust of wind blew his chair and racquet bag across the court.
The Czech laughed at the impossibility of playing tennis in such conditions but on they went and Murray duly wrapped up the set.
The Scot, who was being watched by countryman Sean Connery, began the third set as he had the second, with a break of serve, as Berdych shot an exasperated look towards his supporters.
Murray's greater variety and tactical acumen suited the conditions much better than the Czech's raw power and another break for 3-0 gave him a firm hold on the match.
Mentally, Berdych seemed to have gone walkabout and, although he saved four set points at 1-5, a fifth arrived and this time the Czech drilled a forehand just long.
Berdych's hopes of making a second grand slam final were hanging by a thread, and they took another hit when Murray broke again in the second game of the fourth set.
The sixth seed stopped the run of games against him at five, saving more break points, and that seemed to revitalise him as he then created a rare opening on the Murray serve and took it.
Suddenly it was a match again, albeit one that was still very much in the third seed's hands, but if he was going to win it in four sets it would have to be in a tie-break.
Murray was unfortunate that he started the game at the more difficult end and Berdych raced into a 4-1 lead, but the Scot recovered the deficit when they switched ends, levelling at 5-5 with an angled backhand return.
Berdych played a good point to move 6-5 in front but Murray saved the set point and then brought up his first match point only to see the Czech fire down an ace.
Berdych erred with his forehand, though, to give Murray a match point on his own serve, and another mistake from the Czech sent his opponent leaping around the court in delight.