Cook pasta according to package directions. Drain, reserving 1/4 cup of the cooking water, and set aside.
Meanwhile, in a large bowl, stir together the yogurt, Parmesan, 1 teaspoon lemon zest, salt, and pepper.
Cut the zucchini into thin strips about 3 inches long and 3/4 inch wide- like a big stick of gum. Thinly slice garlic.
Add the oil to a large skillet and heat over medium-high.
Add zucchini to the hot oil and cook just until wilted, flipping occasionally with a spatula. (The zucchini should be soft and somewhat see-through.)
Use the spatula to push the cooked 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.
Stir in the tomatoes and cook another 2 minutes or so until softened.
Add the zucchini mixture and the pasta to the yogurt mixture, and toss gently to combine. If too thick, add the reserved water a tablespoon at a time until the desired consistency is reached.