Gonzalez will take on Slovakian fifth seed Dominik Hrbaty in Saturday's semis with Argentine second seed David Nalbandian coming up against Cypriot qualifier Marcos Baghdatis.
After celebrating a milestone win over compatriot Tim Henman in the tournament's opening round, Murray was unable to pull off a further upset against the erratic Gonzalez.
"I'm a bit disappointed because I thought I was serving as well as I did in the other matches, but not doing so well in the rallies," Murray told reporters.
"I'm happy with the two wins I had here but not with the way I played - but I suppose it's a good sign when you're beating top 50 players without playing your best tennis."
In an entertaining and evenly-balanced start to Friday's quarter-final, the 18-year-old dropped just two points in his first three service games.
Gonzalez then upped his game however, and was rewarded with a deserved and decisive break in the seventh game.
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The hard-hitting Chilean struck back emphatically in the third set however -- breaking Murray twice while conceding just four points off his own serve.
Facing three match points on Gonzalez' serve, Murray managed to save two but was finally undone by a service winner.
NALBANDIAN CRUISES
Nalbandian had a much easier time, booking his semi-final berth with a 6-2, 6-2 win over Thailand's Paradorn Srichaphan.
The world number 10 needed just 58 minutes to wrap up a victory that keeps him on course for his fourth successive Swiss Indoors final.
Baghdatis -- the world number 85 - meanwhile overcame Argentina's Jose Acasuso 6-7, 7-6, 6-3 to secure his first ever place in an ATP semi-final.
Despite the gap between the two players in the world rankings, Baghdatis could provide Nalbandian with quite a test.
The former Australian Open juniors winner came close to an upset against the Argentine at this year's French Open -- taking the opening set 6-0 before losing the next three 6-4, 6-4, 6-4.
"I played pretty well in that match, though at the start it was like Nalbandian wasn't there," the 20-year-old recalled.
"Then suddenly he was there and we had quite a fight. He's a great player who plays a lot of rallies and runs well, but I think I can find a solution on Saturday."
Nalbandian is hoping that his fresher legs will help carry the day. "Of course it helps playing a short match today as I know I have an advantage tomorrow," he said.
"He's coming from qualifying, having had a lot of matches and a lot of time on court. Tomorrow he doesn't have anything to lose though so maybe he will be a very tough opponent."
