Berdych has given Murray a lot of trouble in the past and had won six of their previous 12 meetings, but the Czech was left bewildered by the brilliance of Murray as the world No 2 triumphed 6-1, 6-3.
Djokovic was given his sternest test of the week by Bernard Tomic but still came through in straight sets, 7-6 (8/6), 6-1.
Murray said: “I felt like I dictated all match and, against someone who hits the ball as big as Tomas, that’s not always easy to do. I felt like I wasn’t having to do much defending – I was really going for my shots. In the second set I felt could have won all of the games.”
Berdych, who is coached by Murray’s former right-hand man Dani Vallverdu, held serve in the opening game of the match but from there the Scot took over. A forehand wide from Berdych gave Murray his first break of serve for 2-1, and the Scot then came through a test when he confidently saved two break points. He made it three breaks and six games in a row to take the opening set, with Murray’s clean hitting and accuracy from the baseline simply too much for Berdych to handle. It was not until he was 3-0 down in the second set that Berdych finally stopped the rot after losing nine games in a row. But Murray was not about to allow a shift in momentum and served out the victory after an hour and 19 minutes.
Djokovic has not lost a set since the US Open final and won the title in Beijing last week.
Murray trails the world No 1 19-9 in their head-to-head matches but ended an eight-match losing run in their last meeting in Canada in August.
“It will be an extremely tough match,” Murray said. “Novak has played great tennis all year but especially the last couple of weeks. We’ve played some great matches before in Masters series.”
Rafa Nadal ended a 17-month wait for a top-five victory by thrashing Stan Wawrinka 6-2, 6-1 in their quarter-final.
Not since he beat David Ferrer in the quarter-finals of the French Open last year had Nadal beaten a top-five player.
“Being in the semi-finals is a great result for me,” said Nadal. “I hadn’t played the semi-finals on hard court all year and now I am playing two weeks in a row in the final rounds. That’s a big improvement .”
Nadal will take on Jo-Wilfried Tsonga, who battled past in-form Kevin Anderson 7-6 (8/6), 5-7, 6-4.
Heather Watson lost the last 11 games as her run at the Hong Kong Open came to an end in the quarter-finals against Sam Stosur. Watson, now the British No2 after Johanna Konta’s rapid rise, made a fine start against the former US Open champion and led by a set and 3-1. But from there things went rapidly downhill as Australia’s Stosur clinched a 4-6, 6-3, 6-0 victory .