The 22-year-old from Lincoln and her guide Caroline Powell - who are making their Games debut - clocked one minute 34.28 seconds at Rosa Khutor.
They finished 2.73 seconds behind Slovakia's Henrieta Farkasova and her guide Natalia Subrtova.
Britain's other competitor, Kelly Gallagher, finished in sixth place.
There was drama at the end of the race when Etherington crashed into the hoardings after she crossed the line but after a few anxious moments she got back onto her feet.
"I am delighted with the silver medal, I don't think it's sunk in yet," she told BBC Sport.
"We knew going down that it was a solid run, despite my little jump and crash at the end, but that's all fine and I'm really happy to get down and glad to have that confidence boost for the next four races."
It is Britain's first Winter Paralympic medal since the wheelchair curlers won silver at the Turin Games in 2006 and a first skiing medal since 1994.
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