Ryding made up four places from his first run position of 13th to nudge into the top 10 and secure the second best result for a British men's alpine skier.
Hot favourite Marcel Hirscher, of Austria, crashed out early on his first run and halfway leader Norway's Henrik Kristoffersen also failed to finish his second run, handing gold to Andre Myhrer of Sweden.
Switzerland's Ramon Zenhaeusern took silver and Austrian Michael Matt the bronze.
Ryding's top 10 finish was a career-best result for him and Britain's best since Martin Bell's eighth in the downhill in Calgary in 1988.
He said: "At the start of the day if you'd said ninth I'd have said, it's solid. I had a couple of mistakes there that were a bit costly. I feel I could have done more but I think a lot of other people do as well.
"A top 10 at the Olympics after the dust settles I'll be pretty proud of and in four years' time I will have something to really build on."
Additional reporting by the Press Association
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