Cook the pasta according to the package directions.
Heat the oil in a large saucepan over medium heat. Add the garlic and cook until light brown, about 1 minute. Add the tomatoes and their juices, 1 teaspoon salt, 1/4 teaspoon pepper, and sugar. Bring to a boil. Reduce heat and simmer, crushing the tomatoes with a wooden spoon, until the sauce thickens slightly, about 10 minutes.
Add the shrimp to the pomodoro sauce. Cover and cook until the shrimp are pink and cooked through, about 4 minutes. Stir in the basil. Divide among bowls and sprinkle with the lemon zest.
