The Scotsman took the first set via a tie-break but found himself a break down early in the second.
Despite Edmund’s promising start, the 21-year-old went on to lose three straight service games as Murray found his rhythm.
Murray will now face Spain’s David Ferrer in the last four.
The two British players have met just once before in competitive action, in the Aegon Championships at Queen's Club earlier this year, where Murray came through 6-4 3-6 6-1 on grass.
Murray had admitted prior to the match that he felt “uncomfortable” about the prospect of a showdown with his fellow Davis Cup teammate.
"(On) the day of the match it's always a little bit uncomfortable because, normally, when you see your friends and stuff in the locker room you have a chat, joke around a bit, but on match days it always tends to be a little bit more serious," Murray told the ATP World Tour website.
"Once you get out on the court and start competing, it's fine. After the match, again, it's always fine.
"But it is just sort of the couple of hours before when you see each other in the locker room, it can be a little bit uncomfortable."
The 29-year-old has cruised his way through the tournament so far, despite returning to action this week after suffering a thigh injury when playing alongside Edmund in Great Britain's Davis Cup semi-final defeat to Argentina in Glasgow last month.
The world No.2, who is the top seed at the China Open following the withdrawal of world No.1 Novak Djokovic, coasted through Wednesday's second-round contest against Russian Andrey Kuznetsov, winning 6-2 6-1 in one hour and 16 minutes.
As for Edmund, the Yorkshireman defeated Spain’s Roberto Bautista Agut 6-4 4-6 6-4 to make the last eight. Despite losing to Murray, he now looks set to move into the world's top 50.
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, with Edmund producing an excellent forehand winner to deny the Scot.
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.
Additional reporting by PA.Reuse content