The reigning world champions finished just 0.86 seconds behind Slovakia’s Henrieta Farkasova and Natalia Subrtova, who successfully defended their Sochi title.
Knight said afterwards: “I can’t stop smiling. It is the best feeling in the world.”
The 19-year-old suffered a bad crash at last year’s World Championships, said despite feeling initially nervous: “Once we pushed out, it was purely about doing what we had to do and thinking about the technical aspects down the course.”
Wild added: "We've been working so hard all season, but we've been so far away from Henrieta and Natalia so to cross the line and see we were only 0.8 behind, we knew it was a good run.”
The pair will compete again in the Super G on Sunday.