The dual Grand Slam champion, seeded six, beat the seventh seed 6-7 (6/8), 6-0, 6-3, 7-5 and will play either Novak Djokovic or defending champion Stan Wawrinka in Sunday's decider.
The tournament has been a heartbreak Grand Slam for the Scot with three runner-up finishes, but he has given himself another chance to break through and add to his Wimbledon and US Open titles.
The world number six was too strong for Berdych, who wasn't the same player that eliminated Rafael Nadal in the quarter-finals.
After losing a marathon 76-minute opening set in a tiebreaker, Murray finished strongly to clinch the match in 3hr 26min on Rod Laver Arena.
There was plenty of friction between the two and a few glares at each other at changeovers during the opening set sparked by Berdych's decision to hire former Murray team member Dani Vallverdu as his coach.
"I was disappointed to lose the opening set after I had a couple of chances at the end but I felt I was playing better as the set went on and I was very aggressive at the beginning of the second set," Murray said.
"I got more comfortable with the conditions and with Tomas's ball, in the beginning I was feeling quite rushed and then I got more aggressive and made him do more running."
Murray admitted there was extra tension in the match caused by the attention over Vallverdu in the Berdych camp.
"A lot was made of Dani working with him. Me and Dani have been friends since we were 15 and I felt that was a little bit unfair and unnecessary. There is more to life than sport," he said.
Murray broke Berdych's serve six times and hit 40 winners, while Berdych served more double-faults than aces.
The Czech broke the Scot in the eighth game but was himself broken as he served for the set at 5-3.
Berdych fought off break points in the 11th game but prevailed in the tiebreaker after Murray had set point at 6-5.
It was a psychological lift for the Czech coming out on top after a 76 minute tussle.
There were some sparks when Berdych said 'Good play, Tomas' to himself as he passed by Murray after winning the set to the Scot's displeasure.
But the dual major champion raced through the second set with a triple service break over disengaged Berdych in just 30 minutes.
Murray went on the offensive and broke Berdych after trailing 0-40, hitting a forehand winner to the corner on break point.
Berdych was serving more double faults than aces as the Scot stormed to a two sets to one lead.
Murray's greater variety of shots caused Berdych problems and had the Czech frequently off balance and he got the decisive break of serve in the 11th game, clinching the match with an ace in his next service game.
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