The world No 2 was taken to a first set tie-break by his younger rival and Davis Cup team-mate.
Edmund fought hard in what turned into an epic breaker before eventually losing it 11-9.
The world number number 54 - who will break into the top 50 on Monday when the new rankings are published - continued to earn chances in the second set, earning four break points and grabbing one of them to go 2-0 up.
ATP Beijing
Murray clinches title after Dimitrov fightback
09/10/2016 AT 13:42
But thereafter the Scot was ruthless attacking Edmund's serve, breaking three times to wrap up victory and earn a semi-final spot against Spaniard David Ferrer, who beat Sascha Zverev 6-7(4) 6-1 7-5.
Murray won 100 per cent of points behind his first serve in the first set but was unable to convert his only break - and set - point in the 10th game, Edmund producing an excellent forehand winner with his opponent at the net.
Edmund then surged into a 5-2 lead in the tie-break but was unable to find the killer blow before Murray finally won it 11-9 with another powerful first serve.
After saving a break point in the first game of the second set, Edmund was gifted a 2-0 lead thanks to a double fault from Murray, but failed to consolidate the break despite being 40-15 ahead on his serve.
And although he had to save three break points in the seventh game, Murray was in no mood to take his foot off the gas and broke Edmund twice more to seal his place in the last four.
Across the sea at ATP Tokyo, second seed Gael Monfils edged past Croatia's Ivo Karlovic 7-6(6) 7-6(6) and Marin Cilic ousted Argentine Juan Monaco 7-5 6-1 to progress to the Japan Open semi-finals.
Monfils set up a clash with Nick Kyrgios who eased past Gilles Muller 6-4 6-2 - pulling off a beautiful 'hotdog' volley as he did so.
[WATCH: Kyrgios answers one hotdog with another]
The 30-year-old Frenchman restricted the big-serving Karlovic, seeded seventh, to nine aces and came up with nine of his own to win in an hour 31 minutes.
Fourth seed Cilic, the 2014 U.S. Open champion, struggled on serve but was still too strong for Monaco and the Croatian next faces Belgian David Goffin, who secured a 1-6 7-5 6-2 victory over Joao Sousa of Portugal.
"My serve was a bit up-and-down today. It's something I'll definitely have to straighten out for my match tomorrow," Cilic told the ATP website.
"He returned really well in the first set. In the second after I broke him, I could see that he was having some trouble. It's unfortunate for him since I know he's had a lot of injuries."
Australian Kyrgios, who is yet to lose his serve this week, continued his fine run, firing down 18 aces against Luxembourg's Muller.
"I thought I played great today. I served well, returned well and my engagement level was really good the whole time," Kyrgios said.

ATP BEIJING - CHINA OPEN RESULTS

Quarterfinals
1-Andy Murray (Britain) beat Kyle Edmund (Britain) 7-6(9) 6-2
5-David Ferrer (Spain) beat Alexander Zverev (Germany) 6-7(4) 6-1 7-5
Round 2
Pablo Carreno (Spain) beat 8-Richard Gasquet (France) 5-7 6-4 6-1
3-Milos Raonic (Canada) beat Malek Jaziri (Tunisia) 6-3 6-4

ATP TOKYO - JAPAN OPEN RESULTS

Quarterfinals
2-Gael Monfils (France) beat 7-Ivo Karlovic (Croatia) 7-6(6) 7-6(6)
6-Nick Kyrgios (Australia) beat Gilles Muller (Luxembourg) 6-4 6-2
4-Marin Cilic (Croatia) beat Juan Monaco (Argentina) 7-5 6-1
5-David Goffin (Belgium) beat Joao Sousa (Portugal) 1-6 7-5 6-2
ATP Beijing
Murray defeats Ferrer to set up China Open final with Dimitrov
08/10/2016 AT 11:10
ATP Beijing
Dimitrov upsets Nadal to join Murray in China Open semis
07/10/2016 AT 17:06