Bring a large pot of salted water to a boil. Add the pasta and cook as the label directs; add the beans during the last 2 minutes of cooking. Reserve 3/4 cup cooking water, then drain. Set the pot aside.
Meanwhile, pierce the potatoes all over with a fork. Microwave until tender, about 5 minutes. Let cool slightly, then chop.
Heat the olive oil in the reserved pot over medium-high heat. Add the potatoes, season with salt and pepper and cook, stirring occasionally, until lightly browned, about 5 minutes. Add the pasta and green beans and stir to coat. Remove from the heat and add the pesto, lemon zest and 1/4 cup reserved cooking water; toss to coat, adding more cooking water as needed to loosen. Season with salt and pepper.