Murray will face world number one Roger Federer in the last four after the Swiss player was at his classiest best in unseating a bamboozled Croatian player Marin Cilic 6-3 6-4 in the closing quarter-final at the Qi Zhong Tennis Centre.
Tomas Berdych, the fourth seed, won earlier in the day courtesy of a 6-3 7-6 (7-4) win over the fifth-seeded Frenchman Jo-Wilfried Tsonga.
Berydych will next meet Novak Djokovic, who denied world number 21 Tommy Haas his 500th career win with a purposeful performance in completing a 6-3 6-3 win over the German player.
Haas was an honest trier, but never looked likely to unsettle the second seed the longer the match progressed.
Djokovic certainly had an easier passage than US Open champion Murray did against Berdych's fellow Czech Stepanek, who may be 33 but has clearly lost none of his court craft.
British number one Murray is chasing a hat-trick of appearances in the final of this tournament having beaten Federer 6-3 6-2 in the 2010 final and David Ferrer 7-5 6-4 a year ago.
"It was quite a scrappy first couple of sets," said Murray. "Obviously, the second set I managed to get a break, got a bit of momentum."
Murray has been working with the sports psychologist who helped his coach Ivan Lendl claim his eight Grand Slams and it certainly seemed to help the Scot come through a sticky period against old foe Stepanek, who was appearing in his first quarter-final in Shanghai and threatened to upset the form book by dominating at the net on his way to pocketing the opening set.
Murray was 1/11 with Stepanek priced at 9/1 before the match, but you would never have known there was such a gap between the men for large chunks of a feisty meeting. Of course, Stepanek was involved in a few memorable exchanges in losing to the teenage Murray at Wimbledon in 2005, and there is certainly an edge between these two men.
At one point, Murray cut a puzzled and forlorn figure in throwing his racket to the deck in a fit of pique in dropping serve once in the first set on his way to losing it.
Murray was broken at 2-2 in the opening set as he lost a game of cat-and-mouse with the thoughtful Stepanek in falling 40-0 behind. He saved two breaks points before emptying a forehand into the net to hand his opponent the break. Despite Murray's best efforts coming against his own slightly malfunctioning game, Stepanek would hold on for the rest of the first set to move one set to the good.
Murray continued to apply the pressure to the Stepanek serve in the second set and was rewarded as his heavier hitting saw him recover to break for the first time in leading 4-2.
Murray seemed to have found the key to unlock the unpredictable Czech player when he led 1-0 and 40-0 on the Stepanek serve in the second set, but was forced to watch the world number 41 exhibit his powers of recovery to himself break for a 2-1 lead in the third set.
Despite enjoying the advantage, one always suspected Murray could wriggle clear of any danger and so it proved as his celebrated returning skills finally came to prominence to level at 2-2 before a break to love earned him a 5-3 lead which he was never likely to relinquish.
Murray will be content having regained the level of momentum - if not the magic - that saw him snare his first Grand Slam at the US Open against Djokovic at Flushing Meadows last month to win the next two sets.
Murray holds a 9-8 winning record over Federer in their head-to-heads. This will be their first get-together since those epic meetings in the summer when Federer downed Murray in four sets to win Wimbledon in July only for Murray to deny the Swiss player Olympic gold by winning on straight sets on the same court a month or so later.
Earlier in the Qi Zhong Tennis Centre, fourth seed Berdych notched up his 53rd victory of the season to reach the semi-finals of the tournament for the first time.
"I think it was a really solid game and solid performance from beginning until the end," Berdych said.
"I think the biggest difference between me and Jo was I was able to take the small chances during the first and especially the second set. It was not many of them, but I was able to keep it and convert it on my side."