I thought this was from a Sue Monk Kidd book, but I haven't been able to find the quote. I think the author was looking out a window, and says "I think the world will be saved by beauty", as she's looking at a beautiful scene, and feels that beauty is what gives us the hope to live on when things are bleak.

Dostoevsky's “The world will be saved by beauty.”... Dorothy Day quoted this in a magazine.