Murray, No. 3 in the world, got by Radek Stepanek 4-6, 6-2, 6-3 with a strong finish.
Stepanek had his second break of the day to take 2-1 lead in the third set but Murray broke back. After the set was even at 3-3, Murray truly took over. He lost just one point the rest of the way, including a break at love for a 5-3 lead.
Murray draws Roger Federer in the semifinals. Federer, assured for at least one more week as the world's No. 1-ranked player, got past a stubborn Marin Cilic 6-3, 6-4. Federer seemed in control most of the match but Cilic managed a break in each set, including one when Federer was serving for the match at 5-3. Federer answered with his fifth break and a semifinals berth.
Second-seeded Novak Djokovic turned in a 6-3, 6-3 win over Tommy Haas. Djokovic had lost a mere 12 points on serve in his first two Shanghai matches but Haas managed a break point in each set -- converting both.
Djokovic won 53 percent of the points off Haas' serve and totaled five breaks.
Fourth-seeded Tomas Berdych defeated No. 5-seed Jo-Wilfried Tsonga 6-3, 7-6 (7-4) by saving all four of the break points he faced.
Saturday's semifinals will mark the fourth meeting this year between Federer and Murray. The previous three were all finals with Federer winning at Dubai and Wimbledon and Murray taking the gold medal match at the Olympics. Murray is 9-8 all-time versus Federer.
Djokovic is a dominant 9-1 against Berdych.
Celebrity Families of 2014 [PHOTOS]