Bring a large pot of water to a boil. Add the pasta, and cook about 9 minutes, or according to the package directions. Remove 1/4 cup of the cooking water, and set it aside. Drain the pasta. Set aside.
Meanwhile, in a large bowl, stir together the yogurt, Parmesan, lemon zest, and salt and pepper. Set aside.
In a large skillet, heat the olive oil over medium-high heat. Add the zucchini, and cook just until wilted, flipping them over occasionally with a spatula. (The zucchini will be soft and somewhat see-through.)
Use a spoon or spatula to push the zucchini aside so a space on the bottom of the pan is clear. Add the garlic, and cook for 15 to 30 seconds, until golden but not really brown.
Mix the garlic into the zucchini.
Stir in the tomatoes and cook until softened, about 2 minutes.
Transfer the zucchini mixture to the yogurt mixture, and stir to combine. Add the drained linguine, and toss gently to combine. Add the reserved pasta cooking water a tablespoon at a time, if necessary, to thin it. Divide among four bowls and serve.