Bring a large pot of salted water to a boil and cook the pasta until al dente according to package directions. Reserve 1/4 cup of the cooking water, then drain.
While the pasta cooks, heat the olive oil in a large skillet over medium heat. Add the garlic and chili, and cook for 30 to 60 seconds until fragrant.
Add the crab meat and reserved pasta water. Gently stir and warm through for 1 to 2 minutes, being careful not to break up the crab too much.
Add the drained pasta, lemon zest, lemon juice, salt, and black pepper. Toss well to combine and coat the pasta evenly.
Remove from the heat, stir in the parsley, and serve immediately.